Hmm... with problems like that, its very hard to determine exactly what is causing them...
Some games don't like being minimized, but I'm pretty sure my brother minimises WoW all the time so its not that.
Might have been the video card drivers, but you checked that.
The RAM maybe? How many sticks of RAM have you got in the PC? 2x1GB, or 1x 2? If its the latter, I would be tempted for you to remove a stick and try it, and if that does it, swap to see if the other doesn't, or vice versa.
Or, you could always run a memory tester, to check if any faults occur within the RAM that could easily cause a blue screen and a reset.
You'll need a ISO burner, like Nero, but, its worth a shot. Theres also a floppy disk version if you still have one available.
Simply burn it to CD using an ISO Image setting.
Make sure in the BIOS, its set to run from CD first before the hard drive to stop it from booting to Windows first, and it should run the tester.
My sound card hisses if I do a cold reboot too by the way.