Same happened to my iBook 500. The problem is most likely the "reed switch" that carries power to the backlight. It is a $29 dollar part, but requires sevreal hours of labor. You can either do it yourself and risk your sanity and your computer, or you can pay somebody $300-400 to fix it.
I found a repair shop that would buy my iBook for the parts ($250) and bought an iBook G4.
No regrets.