If putting a jumper wire from the + battery terminal to the
small solenoid terminal produces the starter to turn, then the solenoid is ok, if not then the solenoid is bad.
Do check that the bolt mounting holes/feet on the sol. have good ground contact.
If the Sol. tests good, then you have a wiring problem that you have to follow the schematic/wiring diagram to see where the power is being lost.
One can back track from the sol. to the key source, checking each safety,
wire connection or device that is in the circuit, while the key is turned to the start position.
Do understand that normally, the clutch has to be pushed, and one sitting on the seat and the PTO switch has to be in the off position.
Assuming these safety devices are not already bypassed for testing purposes.
To some, this is intimidatingly, but it is as simple as following a garden hose to find the kink stopping the flow.
The circuit is not rocket science or designed to trick someone, or a mouse maze.
if one approaches it in that manner, it will become apparent what is not functioning as it should.
it is called process of elimination.
Only you can do this checking as we are not there physically, just in spirit.