Mower was running, got off mower, got back on to start mower and nothing. Have replaced battery, switch under seat, selenoid , fuse, and ignition switch. Nothing. No clicks. But, starter will turn when power is directly applied. Please help.

Try moving your blade engagement lever back and forth .
Luck

DG is right, you replaced one safety switch but there are usually 3. The blade engagement has a switch to stop you from starting with the blade engaged. There is also one on most clutch/brake pedal so you can't start while in gear. You almost started with the right thinking. I would have skipped replacing the battery since you could have checked that easily. I would have jumped on the seat switch because it seems to be the first one to go out. You said mower was running and you got off. Did you gloss over a few steps? Did you shut of the blade and also put it in neutral and then shut off the ignition switch? Be sure it isn't something silly like balde still engaged, I hate that when I do it.

Makes no difference if I move the blade engagement leverback and forth

Do you know how to jumper both the blade safety switch and the clutch/brake switch? This would eliminate them from being the problem.