I bought a Cadet 782 at an auction a little over a year ago. It was a CCC-manufactured unit, built for IH, which seems to make it an '81 or '82 model. It has a KT-17 Series II engine. From the git-go, it was very hard to start. Choking the engine per the operator's manual resulted in immediate flooding. Once the engine did fire, it would kick over once, then kick out the starter, repeatedly (what a lousey design this is!). Once I got it running, all was good....for a time. Soon, after mowing for 30 minutes, it began to run rough, basically firing only on one cylinder. Readjusting the carb had NO effect. Both plugs were sooted up, so I installed a spare set. Once the engine was cooled down some, it started and ran fine. Twenty minutes later, it back to the same problem. Days later, the engine just quit. No putt-putt-putt, gasp, gasp like running out of fuel...it just quit cold. I had no spark from the coil at all. So, I replaced the coil, and the engine started on the first crank! I didn't even have to choke it! It had run perfectly ever since. I did then relocate the coil so it isn't sitting on top of the engine, absorbing all that heat!
In reading the starting procedure in the ops manual, especially in the convoluted section regarding cold weather, Kohler knew well that there was a problem with this engine!