Monitor needs to be replaced, you have what is called 'BURN IN', which is common for old CRTs which is why ScreenSavers were helpful to keep turning on and off the pixels randomly so they didn't 'burrrrrrrnnnn' the screen with a constant signal.
If this is on a current LCD, again I would still test with another LCD and see what happens. If it still occurs sounds like the GPU could be faulty, you could try to remove then reinstall the video drivers, but most likely again another hardware piece would need to be replaced.