Hi,
A new logic board will indeed require a matching proximity flex and FACE ID module (both are paired to the mother board).
If you want to use this as an entry into microsoldering, you could try to search for the broken component. From the history of the device it sounds like an IC, resistor or capacitor was nicked off while the battery was being serviced. Your best bet would be to look on the topside of the board around where the battery would sit.
good luck.