I got a furby when they first came out - I remember I really wanted a black and white spotted one but when we went to (all!) the shops they had none, and then TRU had a few and they were all white so I had to get that one. It stopped working not even a year after I got it - the voice box broke or something, it moved it's mouth and everything but you could hear the mechanical noise of the movements, it didn't actually speak anymore.
I left it at my sisters house once and she lived quite far away so it had to stay there for a while and she put it the cupboard her telephone was on (it was dark in there with the door shut to put it into sleep mode and she didn't open the door very much) and occasionally she did have to get something out of the cupboard and it would scare the crap out of her because it would be all 'aaaaaaah' since the opening of the door awoke it from it's refreshing sleep and my sister would be all ^#^&#*()#@)#*%%^@$&$^$^@(&*&@#$^ because she'd forgotten it was there!
I think with corroded batteries you can get a nail file (or a knife etc..) and try to scrape the battery stuff out. I just look it up and there's a how to guide on wiki-how:
http://www.wikihow.com/Clean-Battery-Leaks/Spills they don't say it in the guide but I would guess that after you've done the cleaning you should then wipe it out as best you can with a cloth and then leave it to completely air dry before trying new batteries. I figure that's probably important!