As mentioned before on this thread, use an external monitor.
Here's a very common issue with the iBook (G3&G4). All laptops have a wire bundle leading from the Motherboard to the Display, via the inverter.
Most techs quickly assume one of two things, either the inverer is bad (most common display issue in all model laptops, not sure why). Or, the systemboard, daughterboard or GPU has overheated and failed. Both are fixable in many cases, requiring something as simple as replacing the inverter to something as complex and time consuming as a GPU "Reflow". And, yes, this does apply to Apple Tech's as well.
The true issue, is a bit more illusive, but, quite easily fixed. Provided you can find a "Display Wiring Harness/Bundle" that has NOT come from an already effected unit.
Here in Lies the Rub... The "Display Wiring Harness" is positioned in such a way that after many open's and closes, wriggles it's way loose and becomes pressed against the corner of the hinge (Left Hand Side). This is just enough to cause the wires inside the bundle to rub against one and other causing the outer Teflon coating to become bare in this spot. This is pretty easy to identify, since the outer covering of this harness will be worn or abraded at that pinch point. Although this doesn't always happen, it is often visible. Now hear's the Rub of the Rub, once these wires have made contact, they often cause a "Dead Short" or "Dead Ground" either of these allow the circuit to complete prior to reaching the display/inverter. If this is a "Dead Ground", it most likely has not caused any permanent damage to the board or inverter. However, if this is a "Dead Short" it has completed the circuit without resistance and will most likely result in a fried circuit path on the board or inverter.
So, quick identification of the issue is key in making a proper diagnosis, and not just the immediate "Hands in the Air", "It's dead" conclusion offered by way too many techs.
Quickest solution, with minimal cost, replace the "Display Wiring Bundle/Harness" first (since this will almost always be bad, and if not, you can use it as a diagnositic tool on the next machine). Then the inverter. If the display has not lit up, then you've most likely been left with a bad board. But, at least you have properly diagnosed the issue and are the customers new TECH Hero, or if it's bad news, at least YOU know that you've done this the right way!
Hope this helps, Good Luck