Hey aznbigk
Had the same problem, its the stupidest problem you can have.
You run a game, play for 5-10 mins, PC Monitor Shuts Off but PC is still running under full load, then you must force Shut Down.
After that you can't even play a video file in Full Screen and in the end It won't even let you see the Login Screen, LOL
And more to that, you can't even reinstall an OS, because everytime it gets to a point where you have to configure, the monitor shuts off again and you have to force shut down...
Well your problem is the graphic card

There you go. Go to your manufactuer with your guarante list and have it replaced.
If you have some other PC in your house get that Graphic Card and put it on your PC see if it starts just to be sure it's the graphic card. It's the graphic card 90% tho, because the graphic card actualy shuts off and it doesn't give signal to the Monitor.
Hope this helped
PS: BTW i sticked with this problem for almost 2 years, i suspected the graphic card from the first moment but the problem didn't bother me untill it got to the moment when i couldn't get to the Logon Screen.