Help me diagnose a start issue
 

Yesterday I was stuck in Manhattan on 14th street and 6th ave with a dead starter...had to get car towed by AAA (let's not get started with them). I just got the starter out, but before I did pull it out, I tightened one of the terminal connectors and tried to start the car and it fired up fine. While tightening this nut on the solenoid terminal, the actual solenoid seemed to rotate a bit.

Does this "free play" of the solenoid deem the starter to be bad? It's a reman unit from Advance Auto and they have a limited lifetime warranty...meaning I have only one time to swap the unit out.

Thanks all!