Ah yes. I've seen many of those affected iBooks and Ebay. I thought about getting one and try to fix it... But I was a little concern on some of the methods to fixing it.
http://geektechnique.org/projectlab/726/diy-obsolete-ibook-logic-board-repair
While the link above may be a little drastic solution. It gives you a basic idea of what might be needed, if that's the problem. (Let's hope not.)
Hope you can get the problem fixed.