Laptop Shutdown Hangs


I'm running OS 10.4.2 on G3 Pismo laptop. Lately shutdowns frequently proceed to where the Finder icons and menu go away, and only the desktop background remains -- I've always used the default background -- along with the mouse arrow, which is still responsive as usual to mouse movements. The shutdown routine hangs at that point. Could you tell me how to correct this behavior? Thanks in advance.

My technical level: I've been using Macs since 1990 and am comfortable following detailed technical instructions.
It sounds as if there might two things going on. The first thing is to shut down, restart and then open Applications->Utilities->Console and look at the System Log. It may give you a clue on what is hanging up. Also the Finder will hang on a server that is still connected and not responding.