I did another pass at the logic board today.  I desoldered the battery holder.  Honestly the board might be unsalvageable but I think the physical damage is minimal.  However, at the moment it's missing a few components - Y1 (that piezzo), D1 and possibly D2 and C12.  Anyway, out of curiosity I hooked it all up and turned it on.  I also put a floppy in because I think the HD might be dead.  It wasn't initializable inside my 7100/66 but the terminator resistors might have burned out or something.

The floppy drive makes a short single sound (like a writing sound) which I assume just means power is flowing to the bus (or whatever it's called).  The screen doesn't come on and it won't eject the disk which suggests it's not getting to the ROM.  I took out the smaller 4 of the 8 RAM SIMMS to no effect.

Okay I was typing this message while debugging.  I accidentally hit the CRT control board and popped the little glass nub.  That triggered a gas-rushing-out sound.  I'm assuming I'm done here... (?)