Unless you are good at working on PCBs, and Amiga 2000, I would just track down a replacement motherboard. If you have a version 4.x motherboard, it will be a great upgrade to put in a 6.x board.
I like to tempt fate - I still use a Ni-cad (original) battery. BUT I have re-located off the mothrboard, and keep a very close eye on it.