As promised, here are the photos of the repaired humidifier.


Actually, there's not much to look at, since everything looks almost the same as before.
The major change was the reinstallation of the humidistat above the humidifier (indicated by the red arrow in the wide photo), and an electrical box containing the power converter and wire connections (see the detailed photo showing the electrical box with its cover open).
The humidifier originally came with an adapter that plugged into the wall receptacle, but that adapter no longer worked. So, we made our own adapter and stuffed the contents into the electrical box for safety. A wire with a plug comes out of the electrical box, so it still plugs into a wall receptacle (not shown in the photo).
I'm not crazy about all the wires strung across the furnace to the tool cabinet where the electrical box is mounted, but having the humidifier working again is great, so I'll live with the wires.
I didn't know what a big difference it would make to have the house at the right level of humidity. My nose doesn't feel all dry when I wake up in the morning, the skin on my arms and legs isn't all flaky any more, and the house actually feels warmer even though the thermostat settings have not been changed!
This repair was easy, inexpensive (maybe $40, not including the money I lost on the eBay auction for that dud adapter), and has significantly improved my comfort level in the house. And even though it doesn't really add any value to the house, I'd call this project a success!