I have a 22.5hp sears mower with a Kohler motor. Fully charged battery. Nothing from key turn. Motor turns over briskly if I bypass the solenoid but won't fire up.

First thing to do would be to check the fuse. On most Craftsmans it is usually near the starter solenoid. If you can't find that just follow the red battery cable from the battey to the first place it stops. Somewhere within 6" should be two small wires going to a fuse.