whats the model number? Kohler puts it on a silver tag along with other info, (Model and Spec number) should be SVxxx-xxxx
I'm thinking you may have a valve timing issue, as the courage has twin plastic gear cams. however, try getting some starting fluid, (carb/parts cleaner works fine for this) and spray it in the intake (Through the carburetor about a 2 second burst) and try to start it, if you get the same results as when normal starting, remove the spark plug and spray it in the plug hole, reinstall plug and wire, try to start. If you get good results ( no backfire, runs good for a split second) i would suspect a valve timing issue. Now, If you when you spray the startin fluid in the carb and it runs good, probably a fuel issue.