I agree with canguy. The stator (alternator) and flywheel will most likely need to be replaced. You will need a flywheel puller. Link to service manual - http://www.kohlerengines.com/common/resources/tp_2450_b.pdf

ALL current traveling the circuit between the battery side of the starter solenoid and the ignition key switch MUST pass through the fuse and the ammeter. If you can detect 12 volts at the fuse, and 12 volts at the "B" terminal on the ignition key switch...........then you must also be able to detect 12 volts at the ammeter. If you are checking for voltage at the ammeter by connecting your volt meter or a test light to both posts of the ammeter at the same time, you will not detect voltage. To test for voltage at the ammeter, one lead from the volt meter (or test light) must be connected to a ground and the other lead contacting to a post on the ammeter. Testing should show that voltage is present on each post of the ammeter. The ignition key switch does not have to be on to test for voltage at the ammeter. Here is a comprehensive test procedure for testing the starter control circuit of your tractor. Refer to the image below the procedure for a graphic referrence to the steps. For this, a 12 volt test light will probably be easier to use than a volt meter. So that's how I will describe the tests. The battery must be fully charged for these tests to be accurate and you must make sure there are no blown fuses. Clip the ground of the test light lead to a known good ground, negative post of battery is ok. Confirm the test light works by touching the probe of the light to the battery positive post. If light works, proceed to tests. You might want/need a helper to turn the key switch if you have short arms. Lock the brake pedal and make sure the PTO switch or, or other engaging method is not engaged. Step 1 Find the "S" terminal on the back of the key switch (a white wire). Insert the probe of the test light inside the wire connector where the white wire enters the connector, make certain the probe is deep enough to touch the metal terminal. Turn the key to the START position. The test light should burn. If test light does not burn, replace the key switch. If light burns, go to step 2. Step 2 Touch the probe of the test light to the small white wire on the starter solenoid, turn the key switch to the START position. If the test light burns, the entire control circuit for the starter solenoid is good. If this is the case, move the test light probe over to the large post on the solenoid that has the cable going to the starter. Turn the key switch to START position. If the test light burns now, the starter is faulty, or the cable from solenoid to starter is defective. If the test light does not burn now, the solenoid is faulty. If the first test of the white wire on the solenoid did not cause the test light to burn, go to step 3. Step 3 Find the brake switch and locate the 2 white wires on that switch (there might be 4 wires on the switch, only check the white wires). Turn the key switch to START and hold it in that position. Touch the probe to each white wire. If the test light burns when touched to both wires (one wire at a time of course), the clutch/brake switch is good. This would mean there is an open in the white wire circuit between the brake switch and the PTO switch (the switch on the deck, because you have power on the white wire leaving the brake switch but no power on the same white wire arriving at the solenoid). If you have power showing on just one white wire at the brake switch (with pedal locked down), make sure that the switch is adjusted properly. If adjusting the mounting of the switch does not give power to both wires, replace the brake switch. Now, if you have power at both of the white wires on the brake switch , move on to the PTO switch in step 4. Step 4 Find the white wires on the PTO switch and place the probe on the white wires (one at a time). Turn the key to START. The test light should burn on both white wires. If only one white wire has no power on it when in START position, replace the PTO switch. If you have power on both wires here, but not at the starter solenoid, there is a break in the wire between the PTO switch and the starter solenoid.

Well thanks jim98520, I've been "around the block" a few times (mechanically speaking). I've had "good mentors" (mostly because I sought them out) all my life. But I am not the most important member on this forum, there are many who have spent a lot more working hours in the OPE field than I have. I have posted some incorrect info on this forum myself (sorry about your yard), but USUALLY, the more knowledgeable, experienced members stand me up straight, and I promise not to do it again. I do this because of people like my sister, and some aunts and cousins. People who want to try saving some money by DIY. People who want to have a second or third (or more) opinion about their "ailing tractorwhatever". People who have been ripped off (or think they might have been). This forum gives folks a means of getting info and opinions that they could not purchase for any price (haha, I visited a "website" once that "was charging" for answers! Yuk, yuk....YUCK!) Sorry about whatever circumstances have led to your "censorship" (if that be it). It "chillingly" reminded me of getting "chastised" (along with one of my bosses) at work. I sent an "innocent e-mail" to "a vendor" that contracts with my employer. Well, the contact person at the "vendor" forwarded my request for technical data to his boss who forwarded it to my "boss's boss's boss". Of course, all that trickled back down and first thing I know is my boss's boss is ticked at my boss. My boss (though he knew in advance about my intent) said "I guess we better not do that anymore." I said, "I bet your right about that." You might have to come up with a "different psuedonym" (psst. don't tell anybody at work about it).

It would be helpful if you would post the actual engine Model number and Type number found on the engine itself. But yes, your next step should be to remove the spark plug and check for the presence of compression on the non working cylinder. It is simple enough and effective enough to just place a thumb over the spark plug hole and see if it has enough compression to force past your thumb and escape when you operate the starter. Be sure you move the spark plug cable far enough away that you don't inadvertently check for spark as well (shocking). If you find that the cylinder has no compression, your next step after that will be to remove the valve cover from that cylinder and look for a pushrod to have fallen out of place. I think that is enough for you to work with for now. Report back as soon as you know something.