My little Craftsman lawnmower didn't start this spring. It has a Kohler Courage PH-XT675-2044 engine.
Yes, I left gasoline in the mower over the winter, which likely varnished the carb jets.
Youtube videos and my local O'Reilly's automotive recommended carb cleaner and hitting the carb with compressed air. This did the trick for me.
I started by taking the air filter off - as well as the little plastic air-guide.
Then I used an Irwin bar clamp to hold the engine-enable lever to the push-bar.(danger!).
Then, I repeated the following steps about four times until it worked.
(WEAR GLOVES AND A FULL FACE MASK - Carb cleaner cannot be good for your skin, mouth, or eyes, and it WILL spray on you)
* I sprayed a little carb cleaner in the carb throat.
* I started the mower (running on the carb cleaner) -- If it doesn't start here, check the ignition.
* While the mower is running, I sprayed some more carb cleaner in there to keep the engine running.
* After minute or two of running like this, if it didn't start, I let it stop. Then I put a compressed-air nozzle just past the choke vane and gave it a few good blasts, being careful to avoid getting hit by sprayback.
I repeated those procedures three or four times, and eventually, the engine ran on its own without needing the carb cleaner to keep it going.
I hope this helps someone!