It worked! Knowing I'm no good at soldering, and that there are probably 100 solder joints, I opted for a workaround that I've successfully restored electronics with in the past: a heat gun. Applied at a safe distance against the back of the circuit board, juuuust enough heat to melt and rejoin any cracks or weak joints. Hooked it back up, grounded the connector, *click* *click* *thunk*. Door locks and trunk latch all cycled! Now I just need a remote and I should be good to go.