Hmm, Not a bad setup at all..
Do you know what the error is? Does it BSOD?
Although you can't game, try booting into safe mode and see if it's still happens with media player, etc.
You can check your RAM with memtest. It's a bootable cd that you d/l and burn.
Memtest86.com - Memory Diagnostic
Have yhou checked your disk with fdisk command?
Give the 3 suggestions a try, and let us know.