Probably just a bad screen or inverter or something, I would think that there is no fix other than to replace the screen. But I'm no expert on that type of thing.
The iBook G3s above 500mhz were all manufactured with faulty graphics chips which cause issues with video. Apple may replace the logic board if you badger them, otherwise I can link you to a thread where you can attempt some interesting repairs yourself.
I would like to point out, that when I mentioned that Apple may replace the logic board (motherboard) if you badger them - it's because they may do it for free since it's a known issue.