If we assume the click is the solenoid contacts meeting, that should be putting 12Volts from one big lug from the battery through to come out on the other big lug to the starter motor. That should crank the engine but it can fail if the contacts are burned or corroded too much to make good contact.
I will tell you about an old farm boy trick but consdier it may involve some risk of sparks and you want to be sure to stay away from anything like the fan or other parts that may move when the engine cranks!
That solenoid is just a switch to connect battery to the starter but it does it with power instead of us pushing a switch by hand. If you have good 12Volts on one lug and connect that lug to the other big lug, the starter should turn! When broke and no money or time to go to town for a new starter, it was common to just jump under the old tractor and put an old set of pliers across from one big lug to the other to get it started! I DO not advise using good pliers for this as you get quite a lot of sparks or burned pliers!
But the idea is that if the starter cranks when using pliers but not when it clicks and doesn't start, you have to say the contacts are bad in the solenoid!
A different way to test, is by doing a "jump start" only not on the battery but down on that big lug that goes directly to the starter motor. If it cranks that way, the wiring from the battery down to the start has something wrong to keep it from getting full power! Dirty connections somewhere is a common idea to check.
