How do I clean the corrosion of my Furby Boom’s battery coils?

The actual cleaning is probably best done by removing those screws so you can get the battery tray away from the "Furby", If you are able to do so have a soldering iron and can use it, I'd disconnect the leads from the critter (noting which go where to solder them back in place after you clean it. But if you can't do that no worries, you don't have to it would just let you do it more easily. If you CAN do that then heat some vinegar either in a microwave or on a stove, not hot enough to damage the plastic mind you, just WARM... enough to cover the tray in a small bowl (Don't put the tray into the microwave!) after you've warmed it place the tray into the vinegar and let it sit for a few minutes... you should see the corrosion get eaten away by the acidic vinegar and it should foam up a bit. stirring the vinegar a bit can speed the process. {NOTE both the warming and the stirring are optional, they just speed up the chemical reaction,) After maybe five minutes the reaction should be complete and the metal clean of the corrosion. If not, repeat until it is. You CAN use q-tips and or small brushes to help remove the corrosion, if so you might consider wearing gloves, the vinegar is not strong enough to cause harm to you (You eat it after all) but to keep your hands clean.

Once it is cleaned of corrosion, dump the vinegar and rinse with tap water, then, to neutralize any remaining acidic vinegar residue, add half a teaspoon of baking soda to (again) enough water to cover the tray , stir to dissolve it and soak the tray in it for 3 to 5 minutes, then rinse with tap water again.

Dry.

Once it's dry you should be able to reassemble everything and hopefully they didn't lie in the note. If it still doesn't work, check that the corrosion did not extend to the wires connecting to the tray as well, if so, you might have to replace the bad bits.

If you couldn't disconnect the tray and follow the above steps, that's OK, just do the same procedure carefully using q-tips (cotton buds) a small brush, and dipping the buds in the vinegar , then after the corrosion is clean baking soda solution then water... Dry and pray...

Good Luck!