I got the train running. As it turned out, all it really needed were fresh batteries. The wire I severed was one of the lead wires to the battery. Once I re-soldered that, it was good as new. It’s been decades since I soldered anything, and I was clearly rusty. In any case, it felt good to work with my hands.
The kids were besides themselves when the heard the working train. Of course they were only too eager to set up the tracks and see the train back in action.