Someone there may be able to offer a workable rebuilt battery, a re-used case with new
correct chemical cells inside. So long as the micro-chip controller is in place & re-set so
it reads status as new, a re-built battery may do. Not sure what results you may have by
inquiring of battery or electronic shops that can rebuild batteries for consumer goods.
Most of the cells these kinds of shops use in their 'refurbished' or re-manufactured batteries
are from china or other markets; so their quality could vary. And any guarantee at all would
be a matter of between you and the seller. To match equipment specs, for both iBook & the
charger, would be important; especially if a local company doesn't already offer reman units.
Another item that can affect the charging and power adapter use in between, is the circuit
board known as DC-in Board. These can fail, odd effects including failure to charge. The
battery is first suspect, with a known-good battery other troubleshooting is possible. Also
to have a second known-good iBook G4 similar to yours, helps to test charger/batteries.
•Calibrating your Mac notebook's battery for best performance - Apple Support
•Resetting PowerBook and iBook Power Management Unit (PMU) - Apple Support
•Mac notebooks: All about batteries - Apple Support
•Mac notebooks: Troubleshooting power adapters with a barrel-type connector - Apple Support
•PowerPC-Based Mac notebooks: Identifying the right power adapter and power cord--US - Apple Support
http://www.apple.com/batteries/maximizing-performance/
•iBook G3/G4 Repair guides - iFixit.com:
https://www.ifixit.com/Device/iBook
http://macintoshhowto.com/hardware/how-do-i-get-my-broken-g4-ibook-fixed.html
In any event...
Good luck & happy computing! 🙂