Oh and the battery is good!! Tada after 17 years it still works. Amazing.
I'd still remove it if I were you. Like you, I just resurrected my Amiga 2000 that had been powered on maybe once since 94 or so. The battery had leaked and caused corrosion on the CPU socket, so I got a new board off of eBay (yes, I will repair the old one too at some point), removed its battery, and soldered on wires with a connector so I could use a standard cordless phone battery taped to the outer cage. Works great!
I added a 68030 accelerator and a flickerfixer from eBay and I have it on my desk along with my C128 and some of my PC gear. It has been great fun and now I need to decide what I am going to do next (if anything).