Problem shutting down

[inca power]

I have an Ibook G4 running OS X Tiger, and its not shutting down normally. At first it just didnt shut down at all unless forcing it to do so by holding down the power button. After some work, I am realizing it shuts down if im not plugged into the power supply, just running on battery. Also I made a fake user account and it shuts down correctly using both power sources. This is odd and driving me crazy. What can I do??
Thank you

 

[Satcomer]

Take a look at you Login Items (System Preferences->Accounts, Login Items tab) and also take a look at the logs (/Application/Utilities/Console) an while trying to shutdown have open /Applications/Utilities/Activity Viewer to se if something is hanging the system up.