Jim,
One really common issue with these tractors is that the battery connections get corroded and/or rusted over time and then the battery won't turn the engine over and it also won't get a good charge from the alternator. I'd definitely start by opening all the cable connections and sanding the contact surfaces and re-assembling with a dab of dielectric grease. Replace the fuses – they're cheap and sometimes they can look fine but still be blown. Or check them with an ohmmeter if you have one.
I recommend that you install a relay in the glow plug circuit and another one in the starter circuit. The OEM key switch is not the most robust piece of electrical equipment ever made and putting relays in the high-load circuits takes the strain off the switch contacts. If you do a bit of searching here and on other forums you'll fins threads covering how to do this. Your local auto ports store should carry simple 12 volt accessory relays that will work just dandy.
On my Jinma I had an issue with the voltage regulator not making good contact in the fuse block and that caused the same sort of issue you're having, too. If the fuses all check out and the wiring looks good, you might want to check your regulator.