That's the underside of the A4000 rev B mobo (the clock and battery are on the other side). In fact, I'd be willing to bet that the battery corrosion got underneath and either ate through or caused capacitor C177 (as shown
here, center right-ish area below mouse ports) to blow.
It looks like you may also have some trace damage, and since this is a multi-layer board, there's no telling what kind of damage has been done that we can't see.
The mouse is routed through the HCT166 chip on the top side (next to the HCT174 that typically gets damaged by the battery), so you can do a continuity check to it.
Hate to say it, but this one may take a while to fix...
banzai
