Why does my computer crash?

My computer is fine until I try to play a graphics intensive game, even Mine-craft . Suddenly, there are lots of red dots and lines on the screen and the computer turns itself off. When I try to turn it back on, there are many white dots on the screen and the resolution is set to minimum. But if I leave it alone for an hour or so, it gets back to normal. E-set Nod 32 doesn’t find any virus and I strongly believe the problem is hardware related. What is happening?
I have a two years old computer with a core 2 duo and 2gb RAM and running Windows 7 64bit. The problem occured just recently.