The battery is shot. Even if you were operating on AC power most of the time, the battery was still being used. Without getting deep into the physics of things, let's just say that batteries slowly lose their charge over time, and the laptop was recharging the battery every time it got below a certain level. Fast forward a couple of years and the charge cycles on the battery have likely been used up and then some.
On a unit that old, I'd just recommend removing the battery and taking it somewhere for disposal. If you leave it in the unit, sooner or later it's going to start swelling and do damage to the laptop. If that isn't enough to prompt you to remove it, then not too long after that it will probably explode. I don't know about you, but the prospect of hot battery acid flying around doesn't sound appealing to me.
The unit likely isn't worth paying for a new battery, so just leave it permanently connected to AC power. Honestly, the fact that your iBook G4 hasn't suffered the known issue with cold solder joints around the GPU already, is all the more reason you want to leave that thing as stationary as possible.
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