That does help...
Open your Activity Monitor. Move the mouse, and watch the list of processes. click the drop-down menu to change My Processes to All Processes.
Move your mouse, and watch if any processes stop responding - or processor use suddenly spikes, or even RAM memory sudden shows a large change. I don't know why that might happen, but it could be something to watch, as part of the Activity Monitor...
Could be worthwhile to copy files to a USB drive, or flash drive - watching for that copy process to pause, or even fail... built-in USB ports on a G4 tower will be USB 1.1 - so file copying on the USB bus will be really slow.
How much RAM memory is installed?
Do you have OS X reinstall DVDs for 10.4?
Serendipity is a lucky guess !