I have also had a similar problem but the solution didn't actually reside inside the computer.
I have a computer which requires a bunch of amps to run when I play games. I could browse the web and do other light tasks without issue, but if I wanted to play a newer game that really taxes my HD5870 video card my computer would turn off.
I'd start a game, and I have a little gadget that monitors my video card, and a few seconds after the cards memory and GPU voltage and usage would rise my computer would shut down. I've had a few problems with my computer so I wasn't exactly sure what was going on, but I took a look at what was actually feeding power to my entire system, and I had everything plugged into a power strip that was at least five years old! So I changed the power cord that runs from the power strip to the power supply as a precaution, and I changed the power strip too; she runs like a champ now.
This has been happening for a while, and I never thought about changing the power strip because my monitor and everything else wasn't losing power too, or at least I didn't notice they were.
Now you may be asking yourself why would that make a difference. If the power strip could power the computer on why couldn't it provide power for a game. Well my video card uses just a few amps from the 12 volt line at idle but it uses forty amps when it's doing its job. The power supply can easily create those few amps from the power available from the power strip, but the power strip couldn't provide enough amperage to the PSU when the video card demanded it, so either the video card determined that something was wrong and shut down the computer or the PSU sensed something was wrong and shut itself off, or the power strip cut power to my PSU. Anyway way it happened my computer would shut down.
I just made these adjustments today, so I'm not completely sure I have found the real issue, but my hopes are high. I can't afford to replace a PC Power & Cooling Turbo Cool 850 SSI or an XFX HD 5870 right now so close to Christmas, so it better be the power strip.