Hi adnadeau!
Thanks for writing. My bad in not giving the model. It is a Monitor 1103. Yes, the stick is probably the drive shaft. It has little paddles on each end that fit into slots on the bottom of the motor and into the cylinder in the bottom.
I did take the cylinder out of the bottom of the chamber and tried to turn the rod that comes out of it (that the drive shaft fits into) with a pair of pliers and it doesn't turn hardly at all. I have to really force it and it doesn't turn completely once I get it to move.
I will take it apart again and look at what I think is the impeller? Do you know if there is a diagram of the Monitor pump? The Toyotomi diagram you sent the link to looks similar but not exact. Who is Nelson & Small? I am determined to do everything I can before I give up

Having a diagram would probably help me explain what I think the problem is much more clearly.
I am going to go take it apart again and look at the plastic piece the metal cylinder fits into and see if it might be the impeller? Maybe it is broken.
Thanks for taking the time to respond to my post. I appreciate it very much.
Jenny