I have a yard Man (riding mower)-model 13a16714g401-solenoid clicks when attempting to start,Put on new solenoid and same results.

Check the kill wire that is the small black wire on the coil. Disconnect it, then see if you have spark.

You may have a bad battery. Mine did the same yesterday. Battery was charged but did not have the cranking power needed and my solenoid just clicked. Put in new battery and away it went. Hope this helps.
Mike