Hello Popwars and Welcome!
It sounds like it could be two things. It could be either the lamp behind the screen that has died or it could be the power inverter. I'm not sure how much it would cost to replace the power inverter, but it looks like it would cost about $150 if it is the lamp. If your G4 is less than 3 years old and you have AppleCare on it, you maybe able to get either problem fixed at no charge. I would take it to an Apple store and have someone look at it. Sorry I can't be more help, but I hope you find this useful.
Cheerio
Searay