I use 90%+ isopropyl rubbing alcohol, with a q-tip/cotton swab and a paintbrush. I also have a diamond needle kit, that can scrap off heavy corrosion. Sometimes I'll use an soft toothbrush. Baking soda has abrasive properties, yet it's still gentle on electronics. Apply a small amount to the affected areas of your device, and rub it in to remove stubborn traces of corrosion. Then wipe the surfaces down with cotton swabs or a slightly damp, lint-free cloth. White vinegar or lemon juice also works, Most household batteries contain bases, so acids will neutralize their discharge.
Here is a video that might help with your furby: https://youtu.be/iMfin6TM0dE
Here is another video that might help with your furby: https://youtu.be/dJjl7CvBX2Q
Another video that might help with your furby: https://youtu.be/df9WG38gBLs
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