Don't know if anyone else has had this problem. I have two G4s runing OS X. Only one experienced this problem. After I loaded OSX 10.1.4 on a 867 G4, I could not shutdown with software (logout or shutdown); I had to use the big button. Got my money's worth out of being a Apple Support client by holding one of their techs for two hours to troubleshoot. Bottom line solution: we removed Norton System Works (including Disk Doctor), and that fixed the problem.
[Editor's note: The general feedback around the net regarding System Works has not been positive...]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20020502092436133