Capacitor replacement is often most needed on the logic boards, but you shouldn't restrict yourself to that alone. In my case, I've never made the time to swap out all the caps on my analog boards, but I have encountered some keyboards that locked up the computer due to leaked caps. For example, the IIgs keyboard (beloved by SE/30 owners) has electrolytic caps that often need replacement.

Sounds like your main problem is not the caps, but replacing them is important. Hopefully the leaked fluid didn't eat through any traces. But the only way to test that is with schematics and a digital multimeter in Continuity Check mode.