With the terminals being corroded I will assume you have a liquid acid battery. I recommend looking real closely around the battery especially under it for corrosion from the acid sloshing out of the battery. Depsite having electrolyte levels not overfilled, I found that the acid would slosh out and all over the nose of the tractor making a real mess including corrosion at the terminals. I would hate to think about the damage that might happen from acid being sucked through the radiator.
The solution for me was a switch to an AGM optima style battery with gel instead of liquid acid. These are leakproof and can be mailed full of the "gel". No more new mess, now just recovering from the damage done by the acid.