It’s hard to tell from the pictures of the cable, but this could definitely be an issue with that.
The battery on those talks to the logic board through 2 connections—the bus screw (the giant t5 one that holds the board to the battery board), and this little cable. The screw is to assist in actual power delivery from the battery to the board. The little cable is for all the battery data.
If it’s simply corroded, you may be able to clean that up with some isopropyl alcohol and a cotton swab. But if the cable was corroded, the connector may have been too. It looks like that is the battery side of the cable, so would have had a new connector. I would also make sure the locking tab on both sides of the connector is present and locked. Those little ZIF connectors can be really fussy about connections.