How to fix an unusable iMac G4 monitor plagued by static?
Sounds like some part of the display sub-system (video card or display driver circuitry) has gone bad.

All the iMac G4 "lampshade" models have mini-VGA out ports, get an adapter and try connecting it to an external display.

Caveat -- if it's the display logic circuitry itself (as opposed to the LCD panel driver circuitry), you may get exactly the same static on an external display.