Ask Max: Why does my iBook display go black during use?
I have display problem with my iBook G3 (12™). It has to be precariously aligned otherwise the display goes off. It also gives me similar problem with the display when it is run for extended hours and when it gets hot.
There are a few things that can cause an issue like what you described. It could be a loose cable in between the logic board and the display. It could also be a faulty cable shorting out. There is also a chance that your iBook is part of the iBook Logic Board Repair Extension. If you go HERE and check your serial number as described on that web page you will be able to determine if it is covered for repair. Apple could cover your repair and save you a good sum of money.
Take a look at the link and see if it saves the day, otherwise take it in for service.