My John Deere 214 won't start!!

Hi everybody. I'm new to the forum. A week
ago my Deere 214 garden tractor stopped
running and it won't start now. I had just
filled up the gas tank, and I started the
engine to let it warm up before cutting
grass. It was running fine for about 2
minutes, but then it started idling rough
and eventually it died. Every attempt to
start it, after that, would lead to it
barely running and missing, for about 30
seconds, before dying again. I verified
that the spark plug was firing by grounding
it to the top of the engine and watching the
gap. I made sure the fuel cap vent was
unobstructed. I then removed the float bowl
and found it full of gas. So I thought a
carburetor rebuild might be worth a shot. I
got a carb kit from NAPA; part # 7-02024.
I soaked the carb in parts cleaner and
cleaned it thoroughly. I noticed that the
fuel inlet seat that came with the kit was
different than the one I was replacing. I
showed NAPA and the guy working assured me
that it was the proper kit for my carb and
that sometimes they make design improvements
to the original parts. The carb I have is a
Kohler #26. I reassembled the carb using the
new fuel inlet seat and valve, and set the
idle jet to 2.5 turns off bottom; main jet
to 3.25 turns off bottom. It cranked, but
wouldn't fire. I then set both jets to 1.5
turns off bottom and tried again. It will
fire once, but won't start. It's like it
coughs, but doesn't catch. Then after
trying 4 times, something happened to the
starter. The battery is fully charged, but
when you turn the key the starter relay
clicks once and nothing happens. The
starter is only one year old! Did it get
stuck? This tractor is infuriating me and I
have 2 acres to mow! Please help.

NOT sure what you've got going on, but rest assured your GT didn't just randomly stop because it needed a carburetor kit.

As to the starter, if you have cranked the engine for any great length of time, you MAY have "killed" it, even though you recently replaced it.

If you could find a "tractor buddy" locally with some experience, they could likely tell you what's going on within a minute or two, but lacking that I'm gonna do the best that I can do and post a link to the official Kohler Engines manual for your engine, with lots of troubleshooting information and leave it up to you to peruse it regarding your issues.
K 321 manual

check points for gap and or burnt and be sure push rod for opening points is not stuck or has worn down in lenght,if the condensor and points are original then replace them,if your rebuild on carb is correct then ignition is all thats left..if coil is mounted to side of motor its life time is shortened from the heat of the motor being transfered to it. be sure to check it.