I really shouldn't give in to despair so easily.
It wasn't exactly despair, but I did give up on the dryer and buy a used, refurbished one from an appliance sales and repair company. I told them to deliver the thing and take mine away. It was more or less the same model as mine, though mine had a few more bells and whistles.
A friend suggested that the guy delivering the replacement dryer have a look at mine. I called the store back and arranged it. It's the sort of place where the guy they send out to deliver something is also a competent repairman.
One lug of the dryer cord was corroded, and part of a terminal strip. Nothing else was wrong. I'd bought a big jug of liquid detergent some years ago, put it in a high cupboard above the dryer, and left for a week. When I came back, it had leaked out and covered the top of the dryer -- and a little had gone into the housing. The resulting corrosion had finally proceeded enough...
The replacement dryer never left the truck. My old dryer is working as well as usual.