|Check that the cable where it plugs into the system is not too loose or damaged. Let the monitor and system set powered off over night. Then blow any dust out of it that might have collected on the air vents and inside. Often a rest can give it new life.|
But jugding from (ME + Compaq + 64MB), you have a system that is most likley four years old, or older. Five years is the normal life of these older low cost monitors. So it may be on its last legs before starting to have problems.
It could also be the video adpater over heating in the system. Check that the fan(s) are all blowing air and the vents are not clogged with dust.