You could try to replace the screw, I am assuming Its a 1998 model since the 2012 model has two screws. I advice to replace the screw, or you could try to replace or interchange the battery pack door. If its a 2005 model, I would recommend getting a new battery cover.
[image|2588117]
That is a 1998 furby battery pack, the two metal contacts on the side touches the other terminals to make a signal, so make sure their intact, and clean any corrosion.
[image|2588118]
This is a 2005 furby battery door, the screw easily gets stripped, and broken. The corrosion is harder to clean since the battery pack is so narrow. They sell replacements on etsy: https://www.etsy.com/listing/1091061818/battery-cover-for-emoto-tronic-2005-and
Hope this helps!