Since everything else is working its one of two things.
1-bad solenoid. The solenoid is basically a big ass relay. Find your positive lead coming from the starter (99% of starters are grounded on the engine so it should be the only wire, should also be pretty thick) and follow it to the solenoid, which looks like a small cylinder with 2 large leads bolted on and 2 much smaller leads going to starter button and battery. The large leads will go to your battery and starter. Take a screwdriver or any metal and place it across the large leads, effectively bypassing the solenoid. If the starter magically works, you have a faulty solenoid.
2-bad starter. Theres a hundred things that could kill a starter but well discuss the two most likely culprits. Brushes and permanent magnets (pm's). Brushes are consumable. They transfer electricity and stuff, and make the armature spin using kraut magic. Eventually they wear down where they no longer make contact with the armature. Permanent magnets are permanently attached to tge inside of the case of thd starter. Occasionally they break or just come unglued from the case. Once they contact the armature, it no longer works. Either way, youre gonna have to pull that starter. You can order starter rebuild kit which replaces all the internal consumables. If its the pm's, just epoxy them back in place.
