i had this problem, though it may have a differant cause to your's.
My computer would be running fine, but the screen would go blank, it wasnt the screen itself turning off though.
can you acess the screen adjustment screen (eg. brightness) from your monitor?
if so, then the screen is fine.
What was causing mine was that there wasnt enough power getting to my graphics card. This is because it's a newish (last 3 years) card which has an extra power cable going straight into it.
However, i had lots of power cable splitters being used and there wasnt enough power reaching it. Change around the power cables and it should work fine, or unplug it completely and the Card will run on low-performance mode, but should work fine.