I did finally manage to figure this thing out, and it would have been a LOT easier with documentation.
The Input and Output jacks, with all their associated wiring, are in the wrong chassis holes. They were reversed -- in addition their having been one bad transistor.
I'm betting that someone else had it apart to try to track down the bad transistor, failed to find it, and then reassembled it incorrectly.
So if you ever want to play a mean joke on someone, this is a way to do it.