Probably a loose socket connection to the backlight or the backlight assembly. If you have the ability to take apart a computer LCD display, you can most likely repair it or just replace the entire backlight assembly while it's apart.
Go to
iFixit: iPod, iBook, & PowerBook Parts and Accessories and look up your model G3. Then find the steps which show how to remove and replace the LCD assembly and\or the backlight. On some machines (not sure about the G3) the entire LCD has to be removed before the backlight can be accessed.
It might be a good idea if you're going to remove the LCD to get at the backlight, to just go ahead and replace the backlight with a new one.
Regards.