Frank Thompson wrote:
doing trouble shooting on 3 yo lightly used keyed brush mower.. which is most likely and which is most unlikely candidate for problems.
ignition switch
solenoid
starter

Battery is fully charged & when key is turned to start only a clicking sound occurs

Have you cleaned the connections on the battery with either a post
cleaner or emery cloth? Is the ground connection good on the frame or
wherever? How are all the connections from the battery to the starter?
Can you use jumper cables from your car to turn the starter over
directly? Could it be a problem with one of the safety switches?
These might seem like silly questions but it's easy to overlook
stuff like this. Not a mechanic but I trouble shoot electrical
equipment and many times it's the simpler seemingly obvious stuff
causing the problem.