Well, I have to ask
Are you using the latest version of Panther? (10.3.9).
If not, download the combo update and install it. After each OS update, please repair permissions, and after each permission repair, be sure to restart your computer!
In addition to that, there are other ways to improve the way your computer behaves, like updating prebindings and running daily, weekly and monthly scripts. Although these functions are available through apple's terminal application, there is a GUI application (
system optimizer) which will do these things for you quickly and easily.
Also, you didn't tell us what you see when the computer hangs. Yes, it hangs, but you should be able to open activity monitor and see the current process that takes place at the time your computer hangs. If that fails, do this. Open activity monitor, have it show all active processes, then try to recreate the circumstances that make your computer hang. There must be definitely a process that will be shown to draw some processing power from your cpu. try and locate that. Since only the finder is hanging (that's what I understood from what you said), the activity monitor should be selectable.
Do these things and come back here to show the results.