Follow-up: So it turns out that it was the security system. Apparently the wires that read the resistance in the ignition key must have gotten worn out and they failed. As a result, the car thought that someone was trying to start it with a different, perhaps illegally copied, key. So it shut down the starter and the fuel supply, I think. I took it to a local repair shop where they installed a resistor down at the base of the steering column by splicing it in at a point where the tires weren’t worn. The resistor had to match the key’s resistance. The mechanic told me that the codes had to be cleared and that the key had to be in the run position for ten minutes before this fix took effect and the car could start. It runs good now. The cost of the unneeded starter was about $110 and the repair at the shop was about $80. Not too bad considering that the dealer quoted me $390 to put in a new ignition cylinder with two new keys.