1st a question. When did you last give your system a good cleaning? All the heat sinks and fans? CPU, Graphics card and powersupply especially. Even look at your monitor could its vents be dust blocked and in need or a good air blow?
I'd say most likely your monitor, 2nd most likely your video card, 3rd most likely something wrong at the Operating System level that can be fixed.
Boot into your BIOS screen and just let it sit there (While there monitor your temperatures to see if they are normal). If you have the lines even there then it is most likely the monitor (though it could still be the video card). You can isolate it even further by turning the monitor on alone and seeing if it flickers or anything. If it is the monitor then you might try reducing the refresh rate from the video card and even the screen resolution as even if it has begun to fail you may get life out of it by using it in less taxing modes.
If that all shows the monitor is likely alright then reduce your resolution and refresh rate as your video card could stil be marginal. Uninstall and reinstall your video drivers as Stephen says is good.
Have you looked in your area for computer/electronics liquidators? Sometimes you can get parts and even whole systems far below the price you would expect. One of the ones in my area for example is selling Athlon XP 2400 for $230 (Canadian of course) + taxes and monitors starting at $50. If you have such a local store it might let you replace more than you think within your budget.