The trouble you've noted in removing the battery in iBook G4 is uncharacteristic of the design;
except unless the cell has damage and is swollen, or unless the last time it was installed, it
may have been inserted improperly. The contacts for the battery and the way the cell is made
to pivot into position and be held in by the coin-operated retainer, is almost fool-proof.
There is little mention of removing these batteries in the iFixit.com guide (for 2005 iBook 1.33GHz
12-inch or iBook 1.42GHz 14-inch) which are both similar to earlier white Dual USB G3/G4 models.
https://www.ifixit.com/Guide/iBook+G4+12-Inch+1.33+GHz+Battery+Replacement/693
The battery edge toward the outside of the computer, has a shape that fits into the iBook, so as
to hold that side when the inner section is retained by the locking mechanism. There should be
no interference to hinder the battery's exit. The electrical contacts may have been bent so those
in the computer could be holding that side of the battery in. A forced-removal may damage them.
And sadly, the bottom section of the computer cannot be removed without taking the battery out.
There are screws inside the battery compartment. Depending on the iBook G4 build model you
have, the take apart instructions vary, the last two from 2005 differ somewhat, & each has a page
in the iFixit.com https://www.ifixit.com/Device/iBook_G4 repair guides page. Several models can
run Tiger 10.4.x so that doesn't say which one you have.
It would appear you are looking at a possible repair to the computer once the battery is forcibly
removed to gain access to the probable cause of the battery being in the way. I'd consider asking
some independent authorized Apple repair shop if they have any ideas, as it may be less costly to
pay someone half an hour labor (if they avoid damage to the battery electrical contact, & iBook)
to gain access. Usually these batteries almost fall out, if everything is OK.
•iBook G4 Battery Removal: 18 seconds... with a nickel or quarter, (& maybe a small screwdriver)
https://www.youtube.com/watch?v=yle0flELLkE
Oh, found this bit on how to rebuild the old battery pack, unrelated to removing the jambed cell:
https://www.youtube.com/watch?v=YKyhNkQzE5E
How long ago was the battery removed & replaced? If it were installed incorrectly or with force, the
problem you are now having would be difficult to remedy now. Assuming it was able to run off the
battery, it shouldn't be swollen or damaged. However, I've heard of a battery jamb-up, years ago.
I have the 12-inch 1.33Ghz iBook G4 (mid 2005) & a few others that are similar in design.
So, I'm not sure what else to suggest...
"Sorry about that, Chief!" (Max Smart) 🙂