It is unlikely that unsoldering/soldering the tail motor damaged the ESC on the 3 in 1.

There are only two ways I think that could happen- Heat, but the wires would have melted the insulation and it would take awhile for the heat to travel all the way to the ESC. You would have noticed it (smelled it too). The other would be ESD- if the soldering iron is not isolated from the AC mains it is possible to "zap" anything in the current's path.

As far as the capacitor, if you tested the motor with a battery and the cap is attached, that's not it either. You can test it by measurng the resistance across it. This is not a likely cause but something to be aware of. These small caps don't usually short but rather "pop" when abused and that would be visible.