I found the problem, it was jggimi's #2). One of the fan wires had come off from inside the motor. The solder joint must have been physically weak, and broken when I was cleaning the fan.
So it needs to be soldered back on, but it isn't easy to get at the right spot. I managed to take the fan apart to a large extent, but the last step is difficult. The motor assembly seems to require being removed from the fan housing by spreading a C ring in tight quarters, and I don't have the tool to do it.
Anyway, the nature of the problem is now known and I can slowly ponder the options. Thanks again for the inputs.
