Checy-guy,
If what you are saying is that the starter stays in mesh with the flywheel even after the engine has started up then the problem is in the solenoid. This does tow things it causes the battery to be connected to the starter but it also puts the starter pinion gear into contact with the flywheel. If for some reason the voltage from the battery keeps the solenoid engaged then the starter keeps spinning.
So yes it could be the key is keeping voltage going to the solenoid which you can test by taking the wire off of the starter and hooking a volt meter to the end. Then turn the key like you were trying to start the engine. Then let the key go and if you still have 12volts then the key is the problem.
But what I have found is that when you or who ever put the starter in, caused the "start" wire to come in contact with the run wire at the starter. So when you turn the key the starter cranks but then when you let go of the key the "run" wire keeps battery voltage going to the solenoid which keeps the starter spinning.
There is one other cause and that is the spring on the bendix spring is not retracting the pinion gear away from the flywheel.
What do you have to do to get the starter to stop spinning?
Scholman