To verify the starter, leave the disk out and solenoid out and open, and use something heavy, like a short piece of steel to short across the two contacts where the copper disk would make contact, making sure that you don't hit something else and short it as well.
Obviously, you have to have 12 volts connected to the terminal and the starter grounded, but a good way to do this is with jumper cables if it is out the tractor. Put the black clamp on the negative terminal and somewhere on the case of the starter, and the red ternimal on the positive terminal and the the cable lug on the starter. When you short across the contacts the starter should spin. This will verify that the starter brushes, etc are in good condition and working. If nothing happens, then you have other issues, such as the brushes being bad, which will require disassembling the starter itself to check them. If you don't feel comfortable with this, take it to a starter shop.