Thanks for all the advice. I think I'm gong to try replacing the batteries in the II and see if that does the trick. I know the IIx is a slightly better machine, but the II was my primary machine for probably close to 10 years...and while that was a long time ago, it was good enough for me then and it should be good enough today for the very limited amount of use I expect it will see.

Can I just snip the leads off near the battery, and leave them attached to the board so I can reuse them to solder to the battery holders? That way I wouldn't have to touch the logic board with the soldering iron. Do the battery holders need to be attached to something else for support, or will the soldered wire joint be strong enough to handle a careful battery insertion/removal?