Strange symptoms leading to system hang several minutes after startup

I recently got a very nice G3 Pismo PowerBook that I can't wait to start using. However, there seems to be something wrong with it and I can't quite figure out what it is.

Minutes after booting up the computer, the mouse cursor will suddenly start to move really slowly. This happens regardless of whether I use an actual mouse or the trackpad, and it happens both on the installed Mac OS 9 as well as the Mac OS X installer CD.

The system still works properly, but a little while afterwards (again, several minutes) the system hangs. Both times can vary quite a bit but it usually runs for at least 3-5 minutes before completely freezing.

Another symptom is that I can't use the power button to shut down the computer once it hangs, no matter how long I keep it depressed.

Does anybody have any idea of what's wrong? It seems to work perfectly fine otherwise.