Doesn't hurt to try with the warranty...And keep in mind that different people can get different things out of a warranty. You should be firm and insist that Apple help you with the problem. Don't take no for an answer. Be polite, but don't accept their excuses. Just because the guy on the other side of the line says that it's not covered under warranty, that doesn't mean you can't make it get covered under the warranty.
I'd explain how you've been a loyal fan of Apple over the years and in all your time you've never had the displeasure of having this kind of hardware defect. Macs are made to last, you've always felt, and this surely can't be a common problem endemic to Apple's manufacturing. It must be a mistake and you hope that Apple will do its part and take care of it.