How old is the iBook? If it is old enough, the PRAM/NVRAM battery has died - and removing the main battery while that was discharged can cause the Power Manager to get confused. If that happens, the machine might not turn on.
Flip the iBook over and tell me what the model number on the bottom is.
This happened with my Mom's 2001 iBook. The battery would discharge in about 1/2 an hour. It would not even wake from sleep. However, I removed and replaced the battery (the same 6 year-old battery), plugged in the charger, and then powered up the iBook just fine with the charger plugged in. In fact, you can run an iBook on the charger alone without a battery even in the battery bay.