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,
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