Rather than starting my inquiry by looking directly at disabilitated, I decided to do some research into the term disabilitation, on the theory that if the latter word exists, the former word is almost inevitable.
The old (and young) history of 'disabilitation'
A quick Google Books search turns up several matches for disabilitation in published works. The word is not used consistently in all instances, however—as you might expect, given that the few occurrences are spread across almost 400 years.
The earliest match is from the legal case of Finlason contra her Tennents (July 27, 1626), reprinted in The Decisions of the Lords of Council and Session, in Most Cases of Importance Debated and brought before Them; From July 1621 to July 1642 (1690):
Isobel Finlason being Infeft [enfeoffed] by umquhile [deceased] Gray her Husband, who was Infeft in certain Cottages in Coldinghame by the King, as vacant in his Hands, by the Disabilitation of John Stuart, Son to the umquhile forfaulted Earl of Bothwell, provided to the Priory of Coldinghame ; and by the Annexation of the said Priory to the Crown, pursues Removing against some Tennents, Possessors of the saids Cottages ; wherein the said John Stuart compearing for his Interest, Alledged, that the said Act of Disabilitation and Annexation of the said Priory, which was the ground of the Pursuers [plaintiff's] Husbands Infeftment, was rescinded and reduced by a posterior Act of Parliament, with all Infeftments depending thereon, and are declared null; and the said Act ordained the nullity to be received by by Exception or Reply, and therefore that Infeftment cannot be a Title, whereupon either to Pursue or Defend.
In this case summary, disabilitation is used (twice) as a legal term of art, with a meaning along the lines of "disabling of (or causing to forfeit) a right or possession." A more common term for such disabling in property law might be dispossession.
About 174 years later, Alexander Geddes, A Modest Apology for the Roman Catholics of Great Britain: Addressed to All Moderate Protestants (1800) uses the word twice in the final paragraph of the preface:
—And let it not be argued, that Disabilitation is not Persecution. To the unignoble mind, every civil Disability is a Disgrace; and a disgrace of such a nature, as that every positive persecution, short of banishment or death, might seem preferable. Nay, death itself, inflicted for mere matters of Religion, would be less intolerable: it would be accounted honourable Martyrdom. But civil Disabilitation is accompanied with infamy in this life, without posthumous renown.
Geddes's subject was the prospective repeal of "disabilitating Laws" that severely limited the civil rights of Catholic citizens of Great Britain. The difference from the 1626 Finlason case is very large because here the issue isn't loss of property but loss of various freedoms common to all other British citizens of similar situation (aside from religion).
In any event, the next Google Books match for disabilitation arises 208 years after Geddes's use of it. From a bibliography entry in Kristin Lefebvre, Racial Variation in Level of Amputation Among Individuals with Vascular Disease (January 25, 2008):
Esquinazi, A. (2004). Amputation rehabilitation and prosthetic restoration. From surgery to community reintegration. Disabilitation Rehabilitation, 26(14–15), 831–836.
Evidently, Disabilitation Rehabilitation is a periodical that in 2008 was in its 26th volume of publication (which is normally equivalent to 26 years of publication). IA Google search turns up citations to volumes 22, 27, and 29 of this periodical, but nothing more. On the sketchy evidence here, it would seem that disabilitation is being used to signify something like "state or process of being or becoming physically disabled."
The final Google Books match for the term is from Lucilla de Arcangelis & Hans Herrmann, "Activity-Dependent Neuronal Model on Complex Networks," in Scale-free Dynamics and Critical Phenomena in Cortical Activity (2012):
Conversely, the quiet periods can last seconds and have been attributed to a variety of mechanisms: The decrease in the available neurotransmitter (Stevens and Tsujimoto, 1995; Staley et al., 1998); the presence of an inhibitory factor leading to a disabilitation of the neurotransmitter release (Stevens and Tsujimoto, 1995; the inactivation, or remodulation of the response, of the glutamate receptors (Maeda et al., 1995).
Here disabilitation seems to have no more technical or specific meaning than "disabling." It's difficult to see what the authors have gained from their word choice beyond a specimen that is five letters (and two syllables) longer than it need be.
The recent emergence of 'disabilitated'
A Google Books search for disabilitated finds ten matches for the term—one from 1974, one from 1997, and the rest from 2001–2015. Even within this relative small window, usage of the term is by no means consistent. I'll review the main tendencies in usage here.
First, from Nancy Joyner, Aerial Hijacking As an International Crime (1974):
The Hague Convention embodies a mature legal evolution of international efforts to deter unlawful aircraft seizures. Even so, it is seriously disabilitated by the universally sanctioned municipal right of providing "safe-havens" for offenders under select circumstances. For this reason, it merits more detailed attention.
The meaning of disabilitated here is something like "undercut," "weakened," or "rendered ineffective." None of the other nine instances of the term in Google Books matches follow this would-be line of usage.
From the discussion of R.J. Davies & G.K. Knowles, "Antibiotic Treatment of Chronic Bronchitis," in Developments in Antibiotic Treatment of Respiratory Infections: Proceedings of the Round Table Conference on Developments in Antobiotic Treatment of Respiratory Infections in the Hospital and General Practice, held in the Kurhaus, Scheveningen, The Netherlands, June 15–16, 1980) (1981):
Dr. Gould: I, like Dr. Davies, have been very interested in this disease for some time. I do not think it is necessarily confined to its definition as “The English Disease', and his picture of the grossly disabilitated respiratory crumble, as we call them in the North, certainly could be replicated in Edinburgh and Glasgow.
Here disabiltated seems to imply an advanced an extremely serious level physical debilitation; perhaps the most mysterious thing about the word choice is the question of why Dr. Gould didn't say "grossly debilitating respiratory crumble," since that seems to be the sense of the phrase he was after. Since these were spontaneous remarks, he may have got caught between disabled and debilitated and ended up with disabilitated as a portmanteau of the two.
From Jan Keene, Drug Misuse: Prevention, Harm Minimization and Treatment (1997):
[Griffith] Edwards [writing in 1986] concluded:
For people who are disabilitated simple strategies of social adjustment or psychotherapy (coping mechanisms) might be useful in reversing the 'dependence syndrome'. There is an important contrast here with the benefits of such general strategies for severe dependence, where similar approaches may be expected to lead to remission.
It's tempting to read disabilitated here as a portmanteau of disabled (physically and psychologically by substance abuse) and nonrehabilitated (because still in the grip of addiction)—that is, as a word that might more appropriately be spelled dishabilitated. On the other hand, it wouldn't be unreasonable to infer that Edwards is simply grasping for a fancier way to say "disabled" (whether from dependency or other causes).
From Craig Paterson, The Contribution of Natural Law Theory to Moral and Legal Debate Concerning Suicide, Assisted Suicide, and Voluntary Euthanasia (2001):
In the case of Karen Anne Quinlan, the court concluded that where a patient was in such a profoundly disabilitated condition, and where there was medical support to sustain that life, there could be a decision to withdraw life support. This line of argumentation found in Quinlan was defended in the cases of Superintendent of Belchertown State School v. Saikewicz, Brophy v. New England Sinai Hospital, and the Supreme Court case of Cruzan v. Director, Missouri Healh Department.
Disabilitated as used here seems to mean "severely and perhaps permanently incapacitated, to the point of being unable to survive without mechanical assistance."
From Jennifer Davis, Her Kind of Want (2002):
Wayne spent most of his time reading thick-skinned books by men whose names Elsie couldn't pronounce. He talked about enlightened consciousnesses and the plight of workers, the evils of capitalism and greed. Injustice, real or imagined, disabilitated him with passion. On their dates Elsie would carefully mention laid-off workers or companies crossing over borders or Wayne's father, who owned the car dealership and half the restaurants in town, and Wayne would work himself into a frenzy.
In this novel, disabilitated seems synonymous with "enflamed," "flooded," or "overran." There is no sense that he is actually disabled in any normal sense—indeed, the author reports that in the resulting passion, "He'd dance around the Mustang like a revival preacher, his curls icicle sharp with sweat, his index finger sharper, pointing at some imagined audience, while he sermonized on the horrors of corporations." The author could very well have replaced disabilitated with inspired without misleading her audience in the least.
From the opinion of Lord Mance in the House of Lords, "In re Deep Vein Thrombosis and Air Travel Litigantion" December 8, 2005, in Encyclopaedia of International Aviation Law (2013):
In Blansett v Continental Airlines Inc (2004) 379 F 3d 177 (US Court of Appeals), a passenger on a trans-Atlantic flight in June 2001 suffered DVT [deep vein thrombosis] which left him disabilitated. By that date many international carriers (it appears about half of them) provided passengers with information about DVT, but many, including Continental Airlines, did not: p. 182.
Here, much as in the 1981 instance, disabilitated seems to mean suddenly and gravely disabled.
The remaining four matches for disabilitated that the Google Books search returns are from 2009, 2012, and 20015 (two different books). In these matches, the meaning is much more consistent— and it more or less corresponds to disabled/debilitated/incapacitated (again, as in Dr. Gould's remarks from 1981), though it may suggest that an unusually severe disability is involved.
From Claudia Osborn, Over My Head: A Doctor's Own Story of Head Injury from the Inside Looking Out (2009):
In the crash that ended the skid, his brother was killed and Richard was severely injured. He spent years in a hospital, the first six months in a coma. Later, at a rehabilitation center, he was outfitted with mechanical aids and taught how to walk and speak again.
"When I was disabilitated," he told us, "I was going to Northwestern University."
From Stephen Sutton, Full Circle: Looking at the World Through My Eyes (2012):
When I was nine or ten my father took my brother and I camping. We stayed in a cow field in Dovedale, Derbyshire on a farm. It was fun but I suffered from asthma so had the occasional attacks this disabilitated me a little and I found the walks difficult at times. Despite this I enjoyed visiting the caves and other sites, my brother was always excited to get out and explore and put his foot in cow pat.
From Anca Sarb, Stelian Brad & Ovidiu Stan, "The Innovation in Design Management of Buildings," in Proceedings of IAC-MEM 2015: International Academic Conference on Management, Economics and Marketing in Budapest, July 10–11, 2015 (2015):
In a study conducted by the World Health Organization and the World Bank should that 15% of the globe's population has a disability, including 5% children. They have also concluded that the poorer countries have the highest percent of persons with disabilities. Due to technical advancements and innovation in various fiel[d]s, the desire to include disabilitated persons in society emerged. Starting with the 1990s governments all over the world started elaborating laws to fully include incapacitated persons into society.
In this example, disabilitated seems to have grown directly out of the noun disability, as if the authors were unaware of disabled as an alternative.
From David Peckham, 101 Thoughts from the Word (2015):
In Syria, leprosy would not have caused Naaman to be shunned, only disabilitated. Leprosy did not keep him from achieving a great status. But he knew he was dying.
Conclusions
The word disabilitation has existed for centuries—first as a legal term referring to dispossession of property and (subsequently) to loss of civil rights, and later (long after the legal meanings seem to have vanished from the scene) in a medical context in connection with physical disabilities and/or the disabling of physiological processes. It remains rare in both contexts.
As for disabilitated, it's a word, too—indeed a more popular word (to judge from Google Books match frequency) than the much older disabilitation. The most problematic thing about disabilitated from a reader's perspective is that it seems never to have been comprehensively and coherently defined. As a result figuring out which of the many of the meanings it seems to have carried in the past is the one an author intends in any concrete instance of use.
The most frequently intended sense seems to be a compound of equal parts "disabled," "debilitated," and "incapacitated." But other meanings that would suit particular contexts where the word has occurred include "vitiated," "unable to overcome addiction," "inspired or filled," and, simply, "disabled." Perhaps the main point to take away from this discussion is that when you are flirting with the idea of using a word that is unfamiliar to the vast majority of English speakers and doesn't appear in most dictionaries of English words, it might be wiser to replace that term with more-familiar words that are likely to convey your meaning more reliably.
Best Answer
I'm afraid it's not a real word, and the inability to find it any dictionary will confirm that.
Richard Ayoade used the 9 letters on the countdown board in a humorous manner as, had it been a real word, it would have won.
The episode in question was not a "real" episode of Countdown - I believe it was an episode of The IT Crowd.