Thank all of you for your very sensible suggestions. I have followed most of them. I made an error in reporting clicking; it was only a single click at the solenoid. Also I didn't report that when running the the engine kep t running when ignition switch was turned to off position and key removed. The mower has not been used since last fall.
After taking your most of your suggestions the following info has come to l ight.
Charger is a new Shumacher costing about $95. I set it on 2 amps. When the green indicator light to show when it was fu lly charged came on after several hours my VOM meter show only 10.4 volts . This was from + terminal to ground & not under load.
When I bypassed most of stuff by connecting 10 gauge hot wire from battery to starter the starter did spin or turn but did not engage engine. I'm not sure if I had a good connection on this. When the test took place there wa s not a notable change in voltage.
Battery is a 12 volt 3 amp battery 3 years old & came on the mower new.
I was unable to test electrolyte because my auto hygrometer glass tube woul d not fit in the small openings on the cells. One cell had the pleated mat erial dark in color as opposed to white in the others. The electrolyte app eared to be halfway between the low level mark on the outside and the high level mark on all cells.
Right now my main suspects are keyed ignition and the battery.