Check that the (-) battery cable is securely attached to the chassis and making good contact, as well as that both cables are making good contact at the battery.
Also, the circuit from the key switch to the starter solenoid is riddled with safety switches which don"t make any better contact with age causing low voltage/current to the starter solenoid.
DEERE addressed this with a kit that can be used on a variety of tractors. See link below.
Or, you may simply have to figure out which safety switch or connection is bad and repair/replace it.