It is more likely a bad DC-in board. This is the part of the iBook that houses the port where you plug in the adapter.
Since the green light on the adapter is coming on, that is an indication that the charger is working as it should. If it were dead, you would see no light.
In my experience, an iBook with a bad DC-in board will run from a charged battery, but the iBook will not run when plugged into the adapter, nor will the adapter charge the battery.
The DC-in board in my husband's iBook failed, but we could swap batteries (since I had an iBook, too), and he could use his iBook normally on a charged battery. We swapped batteries repeatedly, allowing my iBook to charge both batteries, until he was able to get his DC-in board replaced.