Sounds like the video cable or screen- (laptop screens do this all the time) if replacing the screen is beyond your ability sounds like you may have a "parts" box.

Look here [http://www.mac-pro.com/Mac-Pro-Online-Store/G4-iMac-Parts-Flat-Panel-700Mhz-800Mhz}

BTW you can buy a just an LCD screen many places online once you have the pertinent data off the back of the display.

Good Luck,

N.