After thinking about this I realized you probably won't be able to turn the engine manually from under the mower because power from the engine must go through a transmission, so scratch that. Be sure the linkage from the shifter to the transmission is properly connected and the trans. really IS disengaged or in neutral when the shifter is in the 'start' position. G'luck!
First check the oil and be sure it hasn't gone dry. Then check the cable at the solenoid (this is where the 'click' would be coming from) that runs to the starter. Be sure it is clean and tight. If you have a meter or 12-volt test light check to see if you are reading proper voltage at the solenoid and, if so, at the cable where it connects to the starter. (If the solenoid clicks it is getting some power from the battery; WHEN it clicks it should relay 12V to the starter. If, with the key in the 'start' position, you don't have 12V at the solenoid output terminal I would suspect a bad solenoid. If it tests good there but not at the starter end of the cable I'd suspect a bad cable.) If you are getting 12V to the starter I'd guess either (1) bad starter, (2) locked-up engine or (3) you are trying to start it with the transmission in gear. (Please don't be insulted; I've done worse!) You might remove the starter and see if it engages and spins without the engine load (be sure it's grounded). If it does, disconnect the spark plugs and remove them from the engine. See if you can turn the motor shaft manually with a wrench from under the mower. If not, the motor is probably locked up. You *might* be able to free it by squirting some good penetrating lubracant (WD-40 might work) into the cylinders via the spark plug ports and letting it sit for awhile, then try to turn it manually again. This may take a bit of time and it may not work at all, but if it works it might save you from having to rebuild the motor.
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