Computer crashes while playing video games?

If I play games for a while mu computer starts to crash. I will either get the BSoD or my computer will lock up. Both times i need to hold down the power button to turn off the computer. If I don't play video games for a long period of time (for a day or 2, maybe) my computer will run video games just fine for a while, then the crashes become progressively worse. This happens only for video games and nothing else. Even small games like Minecraft crash the computer. It usually crashes within 5 minutes of playing, and there's no warning its just a sudden crash.

I have a Dell XPS 8300 (I got it back in 2011)
Intel(R) Core(TM) i7-2600 CPU @ 3.40 GHz 3.40 GHz
12.0 GB RAM
64-bit Operating System

My graphics card is a nvidia geforce gtx 650 ti, but the fan is broken and vibrates. I do know that one time my computer crashed while I was playing COD and my GPU was about 60 degrees Celcius.

Maybe you have low RAM. Try to restart the computer before it crashes or just buy one for like 15- 20 $$.