that sounds like a bad cable issue. It makes me think that a cable has been knicked and has been having trouble passing current. I would start with the cable, and then work to the inverter. Does the screen turn off randomly if you let it sit?

If it does, the inverter is the issue. if it only gets dark/light when you press on it, especially under the keyboard, it sounds like a cable issue. Try opening it up and check the cable going to/from the inverter. It's not exactly simple on the iBook Clamshells, but it's certainly do-able. You may need to remove some screws and such, but if you don't go about mucking with the rest of it, you will be fine.

iirc, the inverter is in the screen, so this makes me think that when you press on the keyboard area, it should not be affecting the inverter (since it's in the Lid/screen)

Still, try the cable.