Couple of things, first off - Elvis is not dead, he just rides a Kubota
As for the clicking noise, try turning on your headlights on the tractor and then crank it over. If the lights start out dim or go dim when you try to crank it, the battery or the corroded cables would immediately be suspect. If nothing happens with the lights, I would start looking at the starter solenoid.
As for it quiting when you were in the middle of using it, to me that sounds like one of the safety kill switches engaged (apparently by mistake). Somebody help me here with Green machines, does this model have a seat kill switch? If yes, I would try shorting out the leads on the seat switch to see if that might be it.
If you have a volt meter and you put it on the starter or battery and they read OK and don't drop at all when you try to crank it, I would be willing to bet that it is a kill switch issue. There are machines with the same type of device on things like the PTO engagement handle where they will not start or turn over if the machine thinks it is has the PTO engaged when you try to start it.