Iv'e been having this problem ever since i got my new graphics card about a month ago, and it's getting worse and worse, and now i pretty much can't play ANY game for 2 minutes+.
Basically, at first when I just got my XFX AMD Radeon HD 6950 2GB, I played Saints Row The Third all week, but then after that, after about 1 hour of gameplay,I'd get a black screen, and my fan speeds up and is very loud. However, I can still hear the game for a minute or two.
At first, I thought it was just a one time thing. So, I decided to play a game called Rfactor, which is a racing simulation, no where near as demanding as Saints Row The Third, and it all worked fine, no crash. So when I decided to play Saints Row again, it crashed after an hour. Then I thought, it must be because it's a more demanding game, and thought of the possibility of over heating. So, I blasted a fan straight into the PC with my case cover off, and it didn't crash anymore.
But now, after coming back from holiday, ANY game will crash, within the space of 2 minutes. Skyrim won't even load, and the racing game will crash within 2 minutes, even if i have the fan blasting air onto my system...
You almost certainly have an overheating problem. Give the inside of your PC a thorough clean-out and all air-vents on the case. Also make sure all fans are running properly. Consider buying a new case with better airflow too.