Megan,
Have you tried a new battery? The next time you have it on, try to check your battery's health. iStat Pro is a great dashboard widget that gives you a lot of information on your computer... including battery health.
http://www.islayer.com/apps/istatpro/
iFixit appears to only carry the 14-inch battery.
[product|IF184-002]
It sounds like you could have an issue with your DC-in board... but that's step number two. It could be your battery connector or even your logic board.
Check your battery health with iStat Pro, then try the battery, then try the DC-in board and then come back here if it's still not working.
[product|IF184-003]
[product|IF183-030]
Choose one depending on which iBook G4 you have: 14 or 12 inch.