Alright let's get this straight:
Computer shuts down randomly while booting a game.
Holds reset button down to supposedly "warm up" the computer.
Tried switching power supplies but it was still having the same problem.
Took out RAM's one by one and ran a Memtest, 100% error free.
Removed both VGA but nothing went wrong.
2 HDD, 1 40GB and 1 60GB.
Plugging in the 60GB will power up the computer for a certain amount of time.
Computer shuts off once again.
Swap cables, and removed optical drives.
Problem still occurring.
Well, this seems to be your motherboard's problem then. It could be that there is a defect in the motherboard that is causing this problem which automatically shuts down your computer.