Starter trouble - anyone have advice?

I recently purchased a 66 Chevelle. Sometimes when I crank the starter, I hear the solenoid click but the starter motor doesn't turn. I crank 3-5 times and it starts (and sounds good). Sometimes the starter won't turn at all...the solenoid just clicks forever. I tried shimming it thinking that would solve my problem. But now it whines before the engine finally turns over...which makes me think I have the starter shimmed too close to the flywheel. The flywheel shows proof of this now with slightly worn teeth. Anyone have advice?

The copper disc in the solenoid is corroded and not making electrical connection. Take it apart and sand the disc shiny. Be careful not to break the wire to the "start" terminal when you take the end cap off. Or just buy a rebuilt one.

You're bendix drive may also be slipping and that is the whine.