Windows crashes during gameplaying!

Just bought a new computer and quickly noticed that I couldnt play graphic intense games for more than 10-20 minutes before the system shut down, leaving no trace whatsoever except a event ID in event viewer:

Event_ID 41: "The system has rebooted without cleanly shutting down first. This error could be caused if the system stopped responding, crashed, or lost power unexpectedly." BugcheckCode 0.

The temperature seems to be fine, the games (starcraft 2, mass effect 2) float perfectly in max settings.

One strange thing was that after a crash had occurred, I first needed to boot in safe mode, or else the system would crash immediately during startup.

Tried a lot of things, updated drivers, bios, windows update, changed graphic card (radeon 5850, thats what Im using right now) and nothing worked.

I thought the problem would be that I had to weak PSU, but then I tried running memtest over night and now Im pretty confused. When I came back next day I had a bluescreen going on, rebooted the system and found a memory dump file.

What the hell is going on!? Why does it give me a bluescreen now and not when Im playing games? I checked of the property that automatically restarts the system during failure. Do I both have some kind of PSU- and memory problem?

Btw, I didnt know that the memtest I ran differed from the test everyone is talking about, memtest86, so thats for you who wondered how I could get a bluescreen during my memory test.