Hi Mike,
Congrats! The 2000 is the hardiest of all the big box Amiga's. That being said you really need to attend to the battery damage.
Definitely remove the battery with a nice accurate cutter.
Pull the motherboard, all socketed chips, and neutralize the battery acid (with Apple vinegar or citrus).
Wash it with distilled water.
Dry it off.
I put baking soda on the are and let it sit, then rewash the board.
Lastly I use radio shacks circuit board cleaner to clean all slot connecters and sockets. (nasty stuff, spray outside).
Put back together and enjoy. One thing to be concerned with is to very thoroughly try to neutralize the acid, the Amiga MB are sandwich boards and corrosion can still destroy traces.
