Hi Union Jack,
Welcome to techimo,
I believe tha problem is your video card and I think you will have to replace it.
Before we do that tho:
1. turn off your computer, open your case and see if the video card is loose. Just gently press the card into the socket, dont jiggle it but gently rock it side to side into the socket. Check to make sure the cable is firnly attached to the card, and to your monitor. Close up the computer and turn it on.
2. If this does not fix your computer Try(If you can ) a different computer with your monitor, if the problem goes away on the other computer it is most likely the video card is the culprit(this is waht I believe to be your problem.
3. If it does NOT go away it is the monitor and you will have to replace it instead of the video card.