Brand New MacBook Pro is DOA

I bought a $3,000 MacBook Pro (17 inch HiRes with 4 GB and a big harddrive) from apple's website and it arrived Wednesday night
the computer will not stay on long, about 5 min or less, before it just shuts off
i called tech support several times yesterday, erase and installed 3 times, the problem still persisted, on the several attempts to do a fourth erase and install the computer would not stay on long enough to install
i tried to bring it to several apple/computer stores today, nobody in town will repair under warranty (only 1 store in the state is authorized)
i am now trying to send it in to apple through the mail, but it will take a few days before they will send me a box to ship it to them and then it will take 10-14 business days before i get that back
also no one in town will let me return it so i can buy a brand new one now
and the computer is not even 36 hours old

Your machine shutting itself off sounds very much like perhaps the fans are not working. That will cause it to overheat very quickly and shut down in order to protect the CPU and other components. (Just my guess.) If you're asking for some kind of assistance here, there's nothing else we can advise you to do. Rest assured, Apple will make it good. Sorry about your troubles and inconvenience. But in any event, sending it back to Apple is your only recourse.

Regards.

You can return it for a brand new one within 14 days... I'd do that, and complain rather a lot while I'm at it.

Apple is pretty good on replacing items if they are DOA. Call them again and tell them it was DOA. Shipping boxes from them usually ship pretty fast. Some times next day delivery.

That happened to me also, with a previous generation MBP. Now I have a penryn MBP.