Have you tried resetting the PRAM? 1) Shutdown 2) Power UP with COMMAND + OPTION + P + R keys held down and keep holding down until you've heard the computer chime 3 or more times.
If it's a G3 iBook, it may have a bad logic board as many of them failed -- even ones replaced by Apple.
On the other hand, it might simply be that the backlight on the LCD is going or has gone out. Or the video cable is loose where it attaches to the Logic Board.