Starter won't spin.
 

Three times in the last three days my starter has failed to spin, turn the key off and try again and it starts. That is until today. We got stuck in a parking garage at drs. office and it wouldn't turn for love nor money. The solenoid would click but no motor. In desperation I kept turning the key off and on for about 30 times and it finally started just like new. If the connections check good can I assume it's the high priced starter motor?

Unless you can find a loose connection somewhere, it does look like a new motor for you.

The brushes get worn; then more & more often they don't make contact. It depends on exactly which pole is lined up when it coasts to a stop. Hitting the starter with a broom handle can make it go - if that works, it's another confirmation of the problem being in the motor.

^^^ agree.
So, to get it started, have someone hold the ignition key in the start position, while 2nd person hits the starter itself with a hammer.
Maybe a hammer blow via a heavy screwdriver - to reach it. I guess a broom will work? If it starts, very likely, get a new starter.

I'm betting it was the solenoid only. But if you bought a new starter, with solenoid, you'll never know.

Keep in mind that most places sell just the solenoid for almost the same price as a starter. But, they warranty the starter, not the solenoid.