Get a flashlight
ok, so by not working, I'm assuming its blank, otherwise you probably would have called it posessed or schizophrenic or such.
to test. Get a good light source, like a flashlight or a desk lamp and then boot the ibook while shining the light, from behind, into the mac logo on the top of the screen. The idea is that the logo is translucent and you need to get light through the back of the LCD panel.
If you see the gray Mac startup apple on the screen, it means your light source is impaired, either with the inverter (what creates the high voltage to start the fluorescent bulb) or the CCFL (the light bulb).
What you do next depends on what you want to pay and what level of comfort you feel playing with electronic devices.
check out
ifixit.com to see what it takes to take apart the computer. If you decide to replace the screen, I'm pretty sure any 14" ibook screen will fit (G4 or G3) but i'm only 90% certain, so you'll need to make sure the screen you buy will work with your G3.
You'll probably get a bunch of people telling you to get a macbook but I don't think your G3 is used up yet and a new screen is cheap (<$100).
