Small Engines (Lawn Mowers, etc.): Lawn Mower Repair, lawn mower repair, department stocks

Question
I have a Kawasaki 9HP RX73 John Deer riding mower that was given to me not running.

When trying to start it, it kept backfiring. I cleaned the carbs and the jets and finally got it running.  When it was running it ran smooth, when I shut it off it won't start again.  Not sure what to check now....could it be an issue with the coil, or do you have any other suggestions?

Thanks  

Answer
How long did you wait to start it the second time.

If it was over night you have a leaking carb.
Replace the plug again and turn the fuel off when you park it. Every time!

If it was just a couple of seconds, you probably need an ignitor. Coils almost never fail.  My parts department stocks 4 ignitors and zero coils. We haven't sold a coil for this mower in 15 years