Motorcycle Repair: 1966 HD starter/bendix, starter solenoid, clutch gear

Question
Ok, I got a new battery for her and the starter does work with the button but only start occasionally.  The rest of the time it 'spins' like it's missing teeth.  

I called a local mechanic and I don't think he knows the older bikes.  

The starter will 'click' like it's trying to start and then every once in a while 'catch' and turn the motor.  What does this sound like to you? Still the solenoid?  I don't have a lot of faith in what the other guy said was the problem.

Thank you for your help!
(When I did get it started I ran it out for a ride and it was wonderful to get her up and running again! Hope I can get the starter going so I can take her more.  The kick starting is hard on old legs.)

Hancey
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Followup To

Question -
I have a 1966 FLH. The starter does not work now.  The problem started when the starter engaged (while starting it with the starter button) and would not disengage (continued to spin the bendix until I disconnected the battery)It has not worked since.  (I can kick start it. Whew!)  

Could it be the starter relay, the starter motor or something else? (and I'm sure the bendix is shot and needs replacing after that) But what would cause it to do this is the first place?

Can I test any of these parts to find out what the problem is without having to replace all of them?  Limited budget
Thanks so much,
Hancey

Answer -
What is happening is the starter solenoid is not releasing. replace it as well as the spring
Good luck and happy riding
Mike

Answer
Check your starter drive which is located inside the primary. Its the part that meshes with the gear on the clutch. Remove the derbly cover and with a flashlight you can see it. Try turning the bike over. Is it hitting the clutch gear and the shaft just spinning and the gear not turning the clutch? If that is the problem then you need a new starter drive unit
Good luck and happy riding
Mike