Ok so the problem is with your graphics card or something else
Do you currently use a graphics card in the problematic computer, or do you plug the monitor directly into the motherboard....(on-board graphics card)?
Some computers don't have onboard graphics chip and need to use a card, but either way we need to determine if your graphics card is faulty
edit: If your computer has both built in graphics chip and a video card, shutdown the computer, unplug it, open the case, pull out the video card and try using the onboard VGA/DVI port instead.....