Have you tried a different monitor, or another PC on that monitor?
If you haven't, do that first.
If another monitor works fine, then your monitor is the issue.
If another PC works fine on your monitor, then something in your PC is the issue.
If the problem persists with a different monitor on your PC, again, your PC is the issue.
Secondly, it really sounds like a graphics card issue more than anything else to me.
Test your RAM as others have stated above, but if that isn't a/the problem then I'd recommend you RMA the graphics card.
Only do this after you've tested the monitor.
Hope this helps