In addition to the ignition switch, likely there's several safety switches in the circuit, and switches and the connections at their terminals don't get any better with age.
You can troubleshoot with a voltmeter, check the battery voltage at the ignition switch before and during an attempt to crank, and not if it drops appreciably, then move on to the next switch in the series 'til you find a significant voltage drop.
Also, John Deere sells a "starting improvement kit", an "ice cube relay" with a simple siring harness included.
The little relay takes less current to activate than the starter solenoid, causing less voltage drop, when it closed, it switches full battery power to the main solenoid.
Your tractor probably isn't on the list of models it's intended for, but it can be used on most ANY machine, if you understand basic electricity.
Kit is part #AM107421.
You can also save some $$$ and gather up the parts and make your own little "harness".