<VV> unusual starter problem

[Michael Kovacs]

1966 Corvair PG. I went to start it yesterday. The starter engaged but felt like it did not want to turn the engine over smoothly (like a weak batter or poor ground) .
Second attempt:  a slow crank again, then a snap sound and the starter was disengaged from the flywheel, but the starter motor ran while the solenoid was not engaging the flywheel. I disconnected the battery...motor stopped.
I reconnected the battery and the motor again ran at full speed. 
I disconnected the battery again and motor made a click sound and did not run. I suppose the solenoid disconnect the switch inside.  I assume the is a problem with the solenoid. Think I'll pull the stated and get a new solenoid.
opinions?