Problem began about two years ago. Sometimes the car would not start if you tried to start it within a few minutes after it had been driven and turned off. It would grind and grind. But, if you waited about 5 minutes, it started. Initially, this difficulty would occur rarely, then more often. It always started if the car had been sitting a long time, anywhere from 10 minutes to overnight, or several days.
About 6 months ago, though, it would not start at all. Luckily, this happened one morning while it was still in the garage. No intermittent problem this time - grind and grind, but no starting. So, we had a mechanic test the main relay, all the electrical connections, and all the fuel connections. He sprayed something in the fuel injector mechanism, and the car started and ran - so he knew everything past that was OK. He said we should hear the fuel pump run for a few seconds when the ignition is turned to ON. But, we heard nothing. To be sure, though, he circumvented the main relay, but still no fuel pump noise. So, we replaced the fuel pump and the fuel filter. After he removed the old fuel pump, he wired it directly to the battery, and of course it ran. He said that kind of thing can happen. Well, OK.
After the replacement was made, the car started. And I turned it off and started it several times, including after driving it for a while. And it kept starting and running fine - for two months. Then, one day after I had been driving for a while, I had to start the car after it had been parked for just a few minutes. Grind, grind, grind, but no starting. Waited a few more minutes, and it started. Same thing happened a month later. I replaced the spark plugs, which had been a bit overdue. Now we're having the same problem with the engine grinding, but not turning over, if the car has only been sitting a few minutes after being driven and turned off. I always listen first to hear the fuel pump run, and it is running - every time, whether the engine starts or not. One other thing to mention - our driving habits with this car: it is mainly used for very short trips in our neighborhood - no more than a few miles at a time, sometimes with several consecutive short trips on Saturday mornings when my wife goes to garage sales.
What do you think the problem is?