Check to see if its the right solenoid.
Last spring I had a solenoid that was wired wrong internally. I could start the tractor by bypassing the solenoid and running a jumper wire to the coil.
One wire that was supposed to be soldered on one side of the solenoid was wired to the opposite side. Ordered one from a different manufacturer to fix the problem.
I think what happened was the solenoid was packaged in the wrong box at the factory. If I flipped it 180 degrees it would have worked on a different starter motor.