My video card control panel has options for a DVI monitor, such as Reduce DVI frequency on high resolution displays. "Check this to resolve display corruption".
I have a Radeon 5870 video card, and Catalyst Control Panel.
And Alternate DVI operational mode. "Enable this if you are experiencing display corruption on your digital display".
Also check the refresh rate, my monitor supports 75 Hz, but I still keep it at 60 Hz.
Use trial and error and see if any of these things help.
Have you always had this problem with this monitor or did it start at some time after working normally.
If so try and role back to an earlier driver and see if that help.
Mike