Small Engines (Lawn Mowers, etc.): John Deere R75 Riding Mower, kawasaki engine, weird problems

Question
I have a John Deere R75, 30 inch Deck riding mower with a 9 hp Kawasaki engine.  I runs great and cuts beautifully!  Only problem is after I have been running it for 5 minutes or more, and the engine has gotten nice and warm - if I shut the engine off and then try to restart it - it won't start.  Won't even turn over or make any noise telling me that it is trying.  If I wait 15 minutes or so, until it cools, it will start right back up.   I can run it all day long until the gas runs out, but if I shut it down, I won't be able to start it until it cools again.  This has got to be a simple fix.  I am almost certain it is not the battery, spark plug or anything to do with vapor lock - which other people have suggested.  HELP!

Answer
How old is the battery?  Have you dis-connected the battery and cleaned the battery posts and cable ends with a wirebrush?

I have worked on that mower years ago but do not remember it well enough.  Starting at the key switch, trace each wire to each safety switch.  Dis-connect each one and reconnect.  I have had weird problems like yours and dis/re-connecting must have cleaned the contacts.

Pay attention to any models that you can't idendify.  I can't remember if the R75 has a safety switch interlock module.  

Let me know if you find any weird modules.
Eric