The starter will engage, but then kick out and just spin until you let off key. When you back off the key, and try again it will keep doing the same thing. Sometimes it will start right up, sometimes I have to cycle the key numerous times to get it to engage the starter and to stay engaged long enough to start the car. Is this the solonoid, or a problem the teeth on starter / ring gear? Any ideas or suggestions would be appreciated. Thank you.

It may be a problem with the starter motor's over-running clutch. If it is, then you'll need to replace the starter motor.

Thanks very much. That is a lot easier than replacing the ring gear on flywheel.