1998 Ford Taurus engine wont start or crank

1998 Ford Taurus, mileage: 94,000. Frequently (As in three times so far this week) this car will not start. All the electrical works, but no crank at all. New battery, two new starters, new alternator, a one year-old air conditioning system. I have had it towed four times recently and every time it starts right up at the service station. The last time they kept it for a week trying to get it to not start. Yesterday I couldn't get it to start. I turned the key to on position, let it sit a minute, then turned to start and it fired up. I got to my destination, and it did this again. My fear is that whatever is happening will get worse, and I am deluding myself that the key has anything to do with it. The Ford garage said I should not have to let the key sit in the on position to start. I am terrified of getting stuck some place. What could be causing this! Ford garage can't figure it out and the problem is that every time it has been towed it starts!