My iBook G4 did something very similar for a long time. You may wish to take a look at this page:

http://www.xlr8yourmac.com/tips/ibookg4_vreg_repair/ibookg4_vreg_repair.html

In a nutshell, the solder joint fractures on one leg of that chip, causing anomalies with the system such as random freezes, loss of video during operation or an inability to boot, among others.

Performing that repair solved my problem. It could also possibly be something else, perhaps something GPU related, but those failures were much less common in iBook G4s compared to the iBook G3. I'd start with the VREG chip.