"Would" and "Will" are both auxiliary modal verbs.
..our store's technicians will fix it free of charge. (=The technicians will fix it free of charge) (surely they will.) (strong probability) (unavoidable)
..our store's technicians would fix it free of charge. (=The technicians will fix it free of charge) but (not strong probability)
We use "Will" to talk about: promises, offers, facts about ability or capacity, habitual behaviour, (for the events that are unavoidable) (definite future)
We use "Would" to talk about: invitations, hope, desire, requests, asking permission, to indicate the consequence of an imagined event or situation. etc.
Would you like to join us? (invitation)
I would like to have a cup of tea. (desire)
(We use "Would" as the past tense of "Will" too but the question is related to the future)
(Note: The question is about "Will" and "Would" and not about "Should". ("should there be any problems with your new computer" means "if you have any problems with your computer")
Best Answer
It's probably the Should there be part that's confusing. Should often indicates some sort of suggestion or obligation, as in: You should take out the garbage. But in this case should indicates something that might happen. Another way to say the same thing would be If there is... So, you could read the whole thing as:
If there is any interest in discussing this further, someone will be in touch with you.
What they're really saying is that they'll take the next step, and you don't hear from them it's because they're not interested in pursuing the matter, whatever that is. That's often expressed as: Don't call us, we'll call you.