310A won't start

Could be several things but if all you needed to do was jump accross the starter selinoid then it's probably a bad selinoid, or wiring to the selinoid. just a quick guess.

You could check for power to the selinoid when the key is on and the starter button pushed in. just hook one side of a (lamp type) tester (or VOM) to the small selinoid terminal that is wired from the start push button and the other to the tractor frame for a ground ( make sure it's to a clean shinny spot for good ground) and attempt to start you should see power( the lamp lights or batery terminal voltage). If you do see power suspect a bad selinoid if you don't then you have a circuit problem.
This could be a bad wire or any of the other starter safety switches that could prevent starting such as:
blown fuse (if in the circuit)
clutch pedal switch
nuetral/park switch
or some other safety item like a seat switch( I'm sure you don't have one of those but you get the idea)
good luck