It would help to know more details about this machine, like exactly which Kohler engine you have.
Also it would be good to know if this engine has a battery & coil type ignition system, or if it is a magneto ignition system.
The symptom you described so far sounds like a problem with the ignition feed circuit to the coil on some VERY OLD battery & coil systems that utilized a ballast resistor to help maintain good voltage to the coil despite heavy amp draw caused by the starter during CRANKING.
I have tried to think of everything you replaced but I'm not coming up with a thing.
Care to share that info? It may help us to learn what all you have eliminated thus far.

Its a K321 Kohler auto coil resistor inside coil.
If you need key switch they are dealer only items they have light switch in key switch and safety wiring ground to switch housing no after market switch like that making dealer item.
You need to join coltcaseingersoll dot com to find dealer.They have all manuals for 444 case hope that helps.

" I have tried and replaced everything I can think of"

You might let us know what you thought of. Maybe you missed something obvious to us?

As mownie stated, know WHICH ignition system you have is important. Some of us "older citizens" have had a lot of experience with various battery/points ignition systems. All we have to do is remember it.
I think mownie & I are thinking the same thing, if it's a battery/points system.
I'm also thinking possible bad capacitor, IF it's that type.

The pin number is 14111472 and the Kohler number is hard to make out but I think it is 1735808423. I have replaced the ignition switch, the points, the coil, the battery, and the starting selonid. I truly thank you for all the help.This is making me crazy.

Have you replaced the condenser (capacitor)?

Chad1969

Your 444 1987 model its 25th edition sticker on side dash tower.
The key switch and solenoid was they purchase from Ingersoll dealer if not want work on your tractor.
Did you join site I listed above so review wiring diagrams and parts book, service manual, operator manual all free info.
This be more like your engine ID numbers.

K321-60410 INGERSOLL EQUIPMENT (14 HP (10.4 kW) SPECS 6006-60443)

I just got a new ignition switch. the one that was in it was not made by case ingersoll. It was a one fits all. I also got an operator's manual. I will try to get it in tomarrow. Thanks for the help i will let you know the out come.

The switch seemed to be the problem. Starts and runs like a bull. Cuts grass like a champ. I should have gotten one sooner. Now i will be looking for a 448. Thanks everyone for the help.

Good job Chad don't for get join that site they have classified section and there 448 on there all time good luck in search for 448 I got 1980 448 that 0ne has hood scoop and 1984 448 that year model had black frame.
You set timing on that Kohler flywheel has S mark with test light. It run better if time take all knock shaking out engine an a lot less noise from muffler.