I have had TWO 2-year-old iBook G4s do this recently -- one that belongs to a teacher I work with, and the other is my grandson's -- and I haven't found a solution. One has a parts-only 3-year warranty, but the other is oout of warranty..

The computer works just fine for a while, then totally freezes. The cursor won't move, downloads stop, any process freezes in the middle. If I reboot by holding down the power button, I get the startup chime, the apple logo against a grey screen and the grey twirly indicating that it is working, but instead of going to the log-in dialog, the whole screen turns solid blue. If I wait a while, I can reboot just fine, but it will freeze again, someetimes fairly quickly, sometimes not for another half hour...

All help welcome!

it sounds like a logic board problem. You can try to do a fresh install of the OS to rule out any software issues causing it, but most likely its a near dead logic board.