Computer Screen Turns of at high resolution when I play games?

Okay , here is the thing. When I start playing video games , no more than after 5 muinits my monitor switches off , but mu computer is still on and i can hear the background music of the game . I have noticed that when i play at resolution 1680x1050 my monitor switches off , but when i play at 1024x756 it doesnt switch off but the graphic really sucks . My Monitor is 22 inch 1680x1050. What can I do to play the games that way ?