You may want to ensure that it's the monitor and not something else. If you can, try your monitor on another machine and try another monitor on the affected machine. This will tell you if the problem is the monitor or the machine.
Sometimes strange things can happen if there are badly behaving electrical devices on the same circuit. Turn everything on the circuit off (printer, fax machine, overhead lights, everything) and see if that clears the image at all. You might also want to try relocating the machine in a different part of the house and see if that makes a difference. This may sound silly, but I remember a person who had a problem with their monitor after they installed a new flourescent light that was introducing interference.
If you try other monitors on the system, and they show the same lines, you most likely have a graphics card issue.
If you try the monitor on other systems and try the monitor in different locations and the lines still show, your monitor most likely has a power supply issue. I believe that this is repairable but, unless your monitor is very expensive, is really not worth the costs of repair.
If you run any of the tests that I describe, please update your post with your findings.