Since we know the fuel shut off solenoid is good I would look at a few carb related items.
1. Inspect the vacum line from the valve cover to the carb for damage(mine was).
2. Inspect carb throttle/choke linkage for proper operation.
3. Remove carb and clean/rebuild.
Here is the link to the Kohler service manual.
http://www.kohlerengines.com/onlinec.../tp_2339_d.pdf