I'm not exactly a technician or anything, nor know enough about computers to give advice, but something like this happened to me as well. Only, it froze up for five seconds then turned off. But for me, I needed a new motherboard. You might want to check to see if you need one of those. Sometimes, when the computer won't turn on (for Dells, at least) if you unplug the power strip from the back of the computer and press and hold the power button for 15 or so seconds, then plug the strip back in, it will turn on again. But, if that doesn't work, I'd suggest calling your provider (whatever company you got the computer from, that is) and ask them to help you out. They'll send over a technician (or you can just take it to some shop to fix it) in about three or so days and they'll replace your motherboard for you.
But, like I said, I'm not exactly a technician. So, I could be wrong... very wrong. XD