Screen comes on but does not light up.

It's a widespread myth that the inverter is the problem in these situations (spread mostly by people who have never done a laptop repair), and 99% of the time it's actually the inverter cable, or the screen itself. With MacBooks and PowerBooks it typically ends up being the screen, however you might want to replace the inverter cable first, since it's a relatively cheap part and there is a chance it's the culprit.

Also, before you start spending money on parts, you'll want to connect the laptop to an external display. If that works fine, you'll have ruled out the logic board as part of the problem, whereas if the external display doesn't work, it's possible you've got a video chip issue.