I had the same problems w/a Kohler Courage 25HP:
1. If you have a charged battery & when you try to start it turns about 90 degrees and stops and it has some age on it, the valves need adjusting. Remove plugs; rotate engine; I put finger in the hole & turned the flywheel till it pushed out my finger on the compression stroke; TDC; I think it is .005 feeler gauge. Mine had a lockdown nut (1/2") w/a allen center set screw. Just a little off and mine would bind consistently; adjusted valves & everything OK. There's 2 10mm bolts @ carb and 2 9mm (I think) on backside to remove engine shroud.
2. Check starter w/plugs removed to see if it is engaging.
3. Check coil to flywheel: .012 feeler gauge.
4. While U R @ it; if it has some age on it; the fuel shutoff solenoid gets gummy w/ethanol gas; clean it while U have it down.
Hope this helps.