If you are "under warranty" they should service. Still, if I went to your home and stole it, why should they fix it for me? Most warranties for computers run about a year. They should have you listed as an owner of the computer. You should have a record (credit card, canceled check, receipt from store) to show you own it. If you are unable to produce such a record, I can almost see their argument...
Proof of ownership demonstrates privity of contract, i.e. that there is a contractual relationship between the buyer and vendor for which the warranty applies. Hypothetically, if the computer were a gift to you from a relative, the relative would be able to exercise the warranty...and yes, show proof of ownership,
If you found this "helpful" or "best answer," please click it with my appreciation.
My response is for educational purposes and does not constitute legal advice nor creates an attorney client relationship which requires all the details and a personal conference.