A known issue with the white G3 iBooks (typically the 700MHz+ units) is the GPU's BGA solder can lose contact with the logic board. Try applying some pressure by squeezing the iBook with your left thumb at the underside left of the trackpad area and power it on. If you see the display come on, even momentarily, then the problem is with the logic board. You can get away with some fixes here like inserting a shim or thermal pad to apply pressure to the GPU from inside the bottom case, or some people have applied heat to the GPU chip to try re-soldering the contacts.
Another possibility, if you were inside the iBook recently, is to try reseating the display LVDS connector at the logic board. If that makes no difference, remove the display rear housing to gain access to the rear of the LCD panel and try reseating the LVDS connector at the LCD.
If that gets you nowhere, the LVDS cable may be damaged and requires replacement. I have witnessed this on my white G3 iBooks in the past. The hinge puts stress on the LVDS and WiFi antenna cables, which can result in glitching or no display image and/or poor wifi reception.