In short, there's four components that determine what goes into Salesforce (assuming stable connections, no weird firewalls that strip data from messages etc).
- The original data
- The mapping of original data to SF Objects
- Triggers etc. in SF
- Access rights in SF
It seems you ruled out 1, 3 and 4 to be the problem, so there's no other conclusion that 2 is the problem.
Check a network analyzer like WireShark to see what is actually going over the line, and try other import tools like DataLoader to check if the import still fails when you know that 2 is good. Possibly, create an Apex Trigger on the Account Object and System.debug(...)
all incoming data, especially the LastName field.
Force.com IDE
Sometimes, you can still login with the Force.com IDE. It doesn't hurt to try. If you can, you can then download the admin profile, update the settings, and you'll be good to go. Make sure you're logging in from inside the corporate network or another location listed on your Network Access list.
Premier Support
If you have Premier Support, call the Premier Support line, and request that the profile be updated by them. They have administrative logins they can use to fulfill your request.
Technical Support
According to 4627, if you've only got one administrator, and that administrator can't login, and all other client options have been exhausted, you can send a letter granting permission to change the system administrator. While it implies that only an email address can be changed, this is not true. Technical Support can remove Login Hours, Login IP Ranges, Single Sign On, Permanent Lockouts caused by too many failed login attempts, and other permissions that can restrict administrative login access.
Not-for-Profit (NFP) Orgs
NFP Orgs can contact the Salesforce Foundation for assistance, as technical support doesn't normally handle NFP orgs (at least, not last time I was involved with an NFP).
Partner Portal/ISV Developer Org
If the org in question belongs is a Developer Edition used by a partner, you can appeal to Partner Support to have the org modified. This would be necessary because Developer Edition accounts can't normally be modified by technical support, but the Partner Support team would probably do so if a partner were no longer able to update/sell their product because of this condition.
Developer Edition
If this is a simple Developer Edition, you're probably out of luck. There's no known process for any arbitrary developer to get back in to an org they're permanently locked out of for any reason. You'd have to create a new org from scratch. Hopefully, you've backed up your metadata.
Best Answer
FIELD_CUSTOM_VALIDATION_EXCEPTION implies there is either a custom validation rule on the object or trigger having some validation (using addError on the field) and this is not due to platform out of box error or a process stopping insertion of content object. To get it running look into the validation rules and create your test data so that it successfully bypasses the validation rule.