A click when you turn the key from the solenoid on the starter is an indicator that your starting circuits are in working order. The issue seems to be that you are mot getting enough amperage and voltage to your starter.
Post #2 did a great job of coveting the usual suspects. If a connection will wiggle on the bolt or terminal, clean it up and tighten it up. Personally for the few minutes it will take, I would pull all 4 main battery connections and check, clean and tighten. Loose and corroded connections can rob voltage and will rib lots of amperage as the resistance to electrical flow has been greatly increased. Few homeowners have equipment to test 12 amps.
You stated you had voltage at the battery but did not say how much voltage. Get a digital multimeter, and check a fully charged battery that has set for 4 hrs or more, you are looking for 12.6 volts. Any thing less, you either have a battery drain (if still connected to the tractor) or a battery that will not hold a charge.
Now if battery holds a charge, it needs to be load tested. Most parts stores that sell batteries can perform this test.
A note on battery chargers: a 10 amp battery charger puts out 10 amps in 1 hour. (Most new chargers have computer chips in them that prevent charging if no amps are present in a battery so you will not be able to charge a dead battery.) While most folks do not have the equipment to test battery amps, you can assume that if the amps on the battery are low enough that the engine will not spin at all, it will take lots of hours to fully charge a battery.
At a 10 amp/hour rate, 10 hours produces a max of 100 amps, so it could easily take overnight or longer ti charge a battery. Another note about that computer chip in the charger, it typically will prevent an overcharging condition.