Help! Random restarts

Recently, my computer's been restarting itself. This usually happens within about five minutes of opening World of Warcraft or Team Fortress 2, so at first I thought it was linked to the GPU but it also does this at completely random intervals, like when I'm on the internet or even when nothing's going on--I leave the computer on at night and I'll sometimes wake up in the morning to see the log in page so I know it's restarted.

It always happens whenever trying to play a game, and only very rarely when doing other things, however. A little while ago, I had the problem of the computer turning itself off randomly. I'd have to pull the plug or switch the power off, wait a few seconds, and try to start it again. To get it running again after it turned off, it would take 3 or so tries of this. Somehow, it stopped doing that and I've got these restarts instead. I'm thinking it may have something to do with the PSU because of this, but I'm still not sure.

Specs:
CPU: Intel Pentium 4 3.20 GHz
RAM: 2x1GB DDR Corsair
GPU: ATI Radeon SE 9200
Audio: Realtek AC'97 Audio for VIA (R) Audio Controller
Motherboard: Phoenix Technologies PT800CE-A
PSU: Elements AP-400X 380W
OS: Windows XP Pro, SP2

I don't get BSOD's when this happens so if there's an error, I don't know what it is.

 

It does sound like the power supply is on it's way out. I would suggest a name brand PSU in the 400-450W range for your system.

 

My hardware suspicions when following occur ...
Restarts ... Memory
Shutdown ... PSU
Their is no golden rule, you travel the process of elimination.