There should also be a fuse on the starter circuit, on the firewall IIRC. Yes there is a starter relay as well, and it too should be on the firewall IIRC. My 1720 has done this two times already and each time it turned out to be the ignition switch........Never could have been the cheaper fuse or relay, always that $70.00 ignition switch.
I actually had to replace my switch 3 times. Two for not starting with the key, and one time when the tractor seemed to act like it had a fuel problem. It would staret to shudder and miss, get hard to crank, and then run fine , and all of a sudden start sputtering again. Full inspection of fuel system revealed nothing. Dealer told me my injection pump was on its way out. It turned out to be the contact in the key switch that feeds the shutoff solenoid in the injection pump. If yo need a new switch save your old keys, I think they are all keyed the same, as all three of my replacement switches and the original were all keyed alike
