Windows Boot Problem

Okay... got a new computer from an auction. Randomly, for no apparent reason, it will turn itself off after roughly ten minutes unless I'm running a music player. Don't know why, but as long as I'm running WMP or something similar, the computer will stay on.

Also, when it shuts down like that, when I reboot, it will get to the windows boot screen before flashing blue really fast before rebooting again. And every time I start it up, it says,  'primary harddrive not found, press F1 to boot from secondary harddrive', or something like that. I had to replace the HD because the original was bad. That screen comes up before the windows boot, and then the blue.

Anyone got any ideas?

The only problem with the suggestion of the HD dying is that it's new... I bought it about two weeks ago and installed it (250 gigs) because the original HD wasn't even registering with the computer. It was bringing up a 'Primary Hard Drive not fount/Secondary Hard drive not found', so it's at least recognizing and allowing the one I have to boot... it just seems really random about when it decides to restart or not.

I keep thinking I should bring it in to Geek Squad, but after they fucking lost my laptop for two weeks after sending it out, only to have sent it to another customer, I don't really trust them.

I'm mostly concerned about the rebooting situation, and the bluescreen I get before it does. And before you ask, I can't read what it says on the bluescreen... it only flashes for a second or two, but it says something about a certain protocol (insert many numbers) not being met. :S