Sounds like either the data cable, or the back light thingy. Possably the graphics card.
If you have a monitor with VGA and DVI inputs, and a graphics card with the same outputs, then you could try seeing if changing the cable makes any difference.
Alternativly, try plugging the monitor into another PC and see if it works.
If the monitor works fine on another computer then it could possably just be a gremlin. A glitch that will come and go every so often. Not alot you can do until the thing breaks full time. But anyway, if the monitor is fine on every other PC but glitchy on yours, then it could be the graphics card.
If it's built in, then ouch. Time to ask Santa for a nice new card. Tell him you've been a good boy, and that Ripsaw will vouch for you on that one.
If it's in an AGP or PCI-E slot then try re-seating the card. Simply pop it out. Blast the socket with the commpressed air duster to make sure the socket is clear of gunk. Make sure the card's plug is grime, grease or corrosion free. I don't think copper oxide can conduct electricity. Then plug it back together and see if you get lucky.
If no joy, try the Junta methord

But as the thing is working, DON'T TOUCH IT!
Good Luck
