You can always replace the screen, and that sounds like what it requires, as it doesn't have the diagnosis that it's the GFX chip, fortunately for you.

I've replaced these screens many times on G4 PowerBooks (A1013, A1085, A1046, A1106, A1138, A1139, etc.) it's not too difficult, and there are many videos online giving instructions on how to do it successfully.

PowerBook Medic in Alabama, USA have some great repair guides/videos that you might find useful, and there are lots more on YouTube, as you might expect.

The tricky part is usually getting the back lid off the surround (and clipping it back on without damaging any of the plastic hidden clips/trim, but using a few thin/flexible knives can be quite useful - it you feel up to the task.