I don't know about the ibook g4, but if it's similar to the g3 version, the backlight inverter gets its power through a power MOSFET switch on the logic board. If you've already swapped complete lids and the problem remains, then the likelihood of this component being the problem increases greatly. IIRC, it's a six-pin surface-mount DIP. You can trace to it from the 4-pin (I think it's four) connector that goes to the lid/LCD assembly. DigiKey sells replacements quite cheaply.