The symptom: Plays on battery but not on AC plugged in.
The failure was the printed circuit trace between the point where the power cord enters the circuit board and the second point where it feeds the power transformer.
The copper traces had vaporized. Both legs. They were totally missing.
The paths had the appearance of overheating.

Fix was to solder jumper wires between the 2 points (2 places)
When charging batteries the current between these 2 points must have exceeded the capacity of the trace to handle the load.