You're not giving people much to go on.
Which model G4 PB?
How much RAM?
How much spare space on HD?
After 15 minutes or after 'a few minutes or so'?
Doing what/with which application(s)/always the same application?
Have you checked in Console and Activity Monitor to see what's happening?
Have you got iStatPro installed to see what's happening with temperatures?
Have you verified HD with Disk Utility?
What does Disk Utility say about HD's SMART status?
Since it freezes after about 15 minutes, my thought is that it's temperature related. Possibly a fan failure.
Download and install the utility Temperature Monitor @ http://www.bresink.com/osx/TemperatureMonitor.html
You may have a bad track pad sensor.
Do NOT open the computer and detach the sensor. There’s no reason to. Here is the complete method for disabling the sensor:
Move (do not delete) the following extensions to a different location (a new folder outside the extensions folder). You’ll find them in your system/extensions folder:
Once moved, restart, and that little sensor will be disabled.