95% of Kohler Command engines have the solenoid mounted on the starter. From the OP original post, my bet is that the plunger contacts are burned. As said earlier, it would be cheaper to purchase a new starter than just the solenoid. Cheapest way would be to have the starter rebuilt, if you have someone in your are who does that. Before you order anew starter through Kohler, check in your area for an auto parts store which handles Denso or Wilson starters. They may be able to get it cheaper for you.