Hi there!
It might be a good idea to just revisit the very basics of any small engine operation... That is to look at 1. Spark 2. Fuel delivery 3. Timing 4. power delivery and safety concerns
1: Spark present?
If you take the spark plug loose and put cable on it and touch to frame and turn it over, do you see a spark on the plug electrodes? If you see the arc, then move on..
2: Fuel delivery
If you take the hose lose at the fuel filter, and put it into a tiny bowl of gas, does the gas suck out of the bowl through the hose you disconnected? The fuel pump on the side of the motor should be able to pull gas steadily here.
4: Power Delivery and Safety Concerns
I skipped to this point because it might be more obvious and easy to test...
Is the PTO engaged for the blades? This might sound obvious at first to check, but there is a switch in the dash that tells the mower that the pulley has been engaged. This would go in conjunction with the RIO switch as well to keep the engine from running as well. You should probably need to check all your switches as these are there to keep you safe. They are all over your mower, so look at your model schematic on the John Deere web page with the wiring diagram for your model.
3: Timing Check
I skipped this one earlier because you will need some kind of timing light to do this to check if you are in time or if you have knocked the engine out of synch.. This is somewhat complicated so I will not go into this here.. I think the #4 is more likely to be your problem anyway.
Check your spark and fuel delivery and then dig into your sensors and switches... GROUNDS are critical here by the way... clean them all up and get some "bulb grease" to squirt into all of your contacts after you clean them up really well. Bad connections or faulty sensor/switches are usually the cause of most issues...
See if this helps you out...