It could be a lot of problems - I'm guessing hardware. Start with the memory. Try only one stick in different slots. It could be other hardware as well such as a bad video card. Since it only seems to do it during graphically intensive activities, it's a distinct possibility.
As you suspect, the PSU might be causing it as well. Once again, since it's happening during heavy graphical loads when the video card is drawing the most power, it could be causing a power failure. Test it out with a more powerful PSU.
It might also be overheating. Check your temps at idle and during load. Make sure all the fans are working and are oriented properly.