1st... Did you check the ground cable from the battery where it attaches to the motor/frame? Remove and clean the terminal with a wire brush?

Could be a bad solinoid not making contact to the starter, are you sure the 'click' is the solinoid and not a safety relay?

Get a test lamp, connect clip to ground or neg batt terminal, have someone turn the key to start while you touch the small terminal on the starter solinoid... if test light lights up power is getting from the battery through the fuse, safety interlocks and ignition switch. If no light then something is not allowing the power to flow to the solinoid.

Next test if you are careful, get a in-line fuse holder and connect a wire to the plus + battery terminal, 5-10 amp fuse in line, disconect the small wire (nut or 1/4" quick connect terminal) and touch the other end of the wire to the solinoid terminal, keeping arms, legs, hair and other appendages clear of the motor. That should cause the solinoid to engage and spin the starter.

Yes/No??

Last test, again real carefull to NOT touch the frame, surrounding metal etc... you could take a jumper cable and connect the two Big bolts on the solinoid if you can reach them, that should spin the starter even if the solinoid is bad. If it Does Not spin, then either the starter is bad or the 'brushes' are worn down and not making contact. Sometimes a little 'thump' with a hammer handle will jar things loose and you will get one-two more starts out of it.

Please post back if you do these tests, AFTER each one! they get progresivly more hazardous to both man and machine, so it's best to do one at a time and get feedback before proceding to the next step.

PTO switch left in the on position..