You haven't mentioned having had the batteries tested. I'd do that next, it may save a lot of otherwise unnecessary troubleshooting. But if that's impractical for whatever reason, start by cleaning all four battery posts AND the associated cable ends. Then top up the battery voltage with a 12 volt charger if you have one. The red wire goes to the + post of the battery that's feeding the starter. The black wire goes to the - post of the other battery. Remove the charger if/when the batteries are topped up. If the batteries won't take a charge, replace them.
If they do - and still can't start the tractor, trace the ground cable looking for defects in the insulation. When you get to the end, unbolt it from the tractor. Scrape/grind/sand down to bare tractor metal, clean the cable lug, bolt it back on. Then trace the positive cable to the starter solenoid, again looking for defects in the insulation. Make sure that connection to the solenoid is clean and tight. Try starting the engine. If that doesn't work, move on to jumping your two batteries with one known good 12v battery. Most car batteries aren't strong enough to start a diesel, so make sure the donor battery has at least 750 CCA.
Put the red jumper cable on the 6v battery post that feeds the solenoid. Put the black jumper cable on the 6v battery post that is grounded to the tractor frame. If that works, you've begun to justify getting a new battery. If it doesn't we're back to my original suggestion that it might be the keyswitch-to-solenoid wiring. To take that out of the equation, first remove the jumper cables. Then take a screwdriver and start the tractor at the solenoid. You already tightened the + battery cable, so you know where that is. Look again at the solenoid and find locate a much smaller post with a wire attached. That's the wire from the keyswitch. Make sure the tractor is in neutral, then touch both of these posts at the same time. It will likely snap and spark, but stick with it until you make good contact between the two. If that doesn't work, it's additional evidence that the batteries are weak. If that works, you've just tracked the problem down to somewhere between the solenoid and the keyswitch.
That too can be remedied, but it's too early to cross that bridge just yet.
//greg//