I'd point the finger of blame are your power supply. Trying running on just 1 stick of RAM (Don't forget to adjust the BIOS setting), alternate sticksto determine if it's still shutting down. If it stays running with 1 stick then the other one is probably bad. If it still shuts down with either stick, then it's probably not a RAM problem (it's highly unlikely that both sticks would be bad). If you only have one stick, go buy another you can always use more RAM =)
Next restart and enter your BIOS setup. In there should be a PC health status, monitor your CPU temperature. While you're in there check your settings and make sure everything is set to the correct levels. Are you getting the gernal idea here? Try to narrow down the problems one by one.
I always use the motto "If it can't be fixed in a handful of hours, reinstall Windows"
Yea, and behold how I have become the Destroyer of worlds.