You need to take out the batteries if you plan on not playing with them. Otherwise, they do tend to corrod the batteries faster. (Then other things in my opinion) They warn about that in all the instructions...
Anyway. You need to open up the bottoms and scrape off all the white/acid off the furby. It should help and hopefully you don't need to go futher inside. If it doesn't wake up, you'll likely need to scrape/clean off the insides under the fur, by the moving gears.
I would also look up "my furby keeps falling asleep" (after being turned on) These instructions should tell you how to remove the fur. If you put the batteries in and find your furby doing the wake up to only fall asleep thing... Follow those directions. Its getting common to find furby that don't "wake up" so those instructions are very helpful if you need them.