I have a John Deere 5210 most likely the problem is the temperature sensor.
On the thermostat housing there is a temperature sensor that is connected to a two wire harness that goes to the injection pump, this is the "cold start advance" portion of the system so it starts easier when cold, the sensor is so it doesn't activate once warmed up. If you disconnect the sensor and it works fine ohm the sensor, probably shorted.
The sensor on the thermostat housing, that controls the advance on the inj. pump. When it fails it shorts out and blows the fuse. Try unplugging it and see if it starts and runs. Double check JD parts, but I thing the part # is RE503242, if you are quick changing it, you don't have to drain the coolant, just make sure it's not hot at the time.
The following are some URLs from the John Deere web-site you may find informative.
The following are the URLs to the 5310 and 540 FEL manuals.
//manuals.deere.com/omview/OMRE71736_19/?tM=
//manuals.deere.com/omview/OMW44993_19/
//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/instrpanelfog.html
//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/leakfuelcap.html
//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/backlash.html
//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/modelyear.html