I have a sears lawn tractor 917.258660 that won't start.

The solenoid justs clicks. I replaced the battery, but that didn't help. The jumped the battery directly to the starter and the engine turned over fine - so I think I eliminated the battery and the starter as the problem.

I then put a jumper from one solenoid post to the other and again the engine turned over.
Does this mean the solenoid is good or bad? The key was off. I traced the wiring as much as possible and by passed the seat switch - all I get is the solenoid clicking when I try to start from the key.

Any ideas appreciated.