What is the condition of the battery?
Go to the System Profiler, then click the power tab.
That will display various information about the battery, such as Full Charge capacity, cycle count, voltage on the battery, charging current, etc.
Full charge capacity for an iBook battery (new) should be around 4800 mAh.
A used battery might still be useful down to around 1500 mAh. Less than a few hundred mAh, would likely only be a few minutes of use.
Compare the numbers that you see from both batteries. You can swap the batteries with power on, just to try. Be sure to refresh the System Profiler window (Command-R), so it re-reads the change in battery. I would probably leave each battery in place for about 10 minutes, just to see how those numbers change. Don't forget to command-R to display any changes. You may find that both batteries don't show any connection, which may mean the internal charge circuit is bad. That MIGHT be the DC-in board (where the power adapter plugs in to the iBook), which can be replaced. Anything else will be the logic board.