Outdoor Power Equipment and Small Engines - Engine won't start

I have a Kohler 19.5 HP engine in my Craftsman gardent tractor. It wouldn't start last year and my Father in law played with the ignition coil I think the arm may have been stuck. It won't start now but the arm is engaging the gears but I don't think there is any spark. Could it be the solenoid? I just charged battery and the battery is < 6 months old.

What "arm" are you referring to? I don't understand your terminology, or the problem here. If the solenoid was the problem, the engine wouldn't even move or do anything when you turn the key. If the coil was the problem, it would still spin, just not start.

Sorry I wasn't clearer. The ignition coil pops up to engag the gears on the larger gear (don't know what to call it) It spins that gear but doesn't start looks easy enough to replace. So if I have it right the fact that the larger gear is spinning and it trys to start would indicate it is the coil? Thank you for your time.

That "ignition coil" sounds more like your starter gear engaging.

Have you tried taking the air filter off and spraying starting fluid in the carburetor?

I was confusing the starter with the coil a friend has cleared this up took much discussion and a few drawings and I think he hit me upside the head a couple of times but I think he got it through my thick head. The starter is engaging and turning the fly wheel. He thinks the coil is more likely the problem.

Well thank your heavy handed friend for clearing that up :D
So the engine spins but does not try to start...?
If you have no spark, the ignition coil is one possibility. Have you tested for spark?
If you have not yet, one test you might try that would confirm spark if you have it. Try adding a few drops of fuel to the carburetor and see if it tries to start or does. If it fires then you must have spark, and most likely a fuel problem causing the no start.
If it does not fire or try to start, then you should test for spark.

Bare in mind that IF you determine that you have no spark, it doesn't automatically mean that the ignition coil is to blame. It could be a bare kill circuit wire, a faulty safety switch, a bad spark plug or an incorrectly gapped coil airgap.

I want to thank everyone for their helpful advice. I cleaned the contacts on shut off switch on seat and replaced a spark plug did the please start dance and it started seems to be running good. Wanted to take it out for a spin but it is 11:23 PM and I don't think my neighbors would appreciate it. Thanks again.

That's good news, thanks for reporting back.