It sounds like a grounding fault. If, as your later reply indicates, swapping out the video card fixes it, the connector on the card is most probably faulty. I've seen the same problem on CRTs as well, usually caused by a bad cable although once or twice it was the VGA card connector. The repeated stresses of connecting and disconnecting the plug, or sometimes just the weight of the cable, breaks one or more joints inside the connector or where it joins the PCB, and you end up with a floating ground. The symptoms are exactly as you describe.

pca