stuck keyboard battery

If the battery has corroded to the keyboards battery contacts (potentially due to leakage), your keyboard may now be scrap. As Apple has not made Keyboards with replaceable batteries for many years, the Keyboard itself may not be compatible with much more recent computers.

If you are unable to remove and replace the battery, you might be best advised to visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to assist:

Genius Bar Reservation and Apple Support Options - Apple

Is your keyboard With external batteries? The rechargeable one is not removable.

For a swollen battery, it can be dangerous to remove so I dont think that if it not goes out, that you should do things like pry in it or so