I know you said the fuses look could, but could you check them again, namely the fuel solenoid fuse. It is on the top second from the left 20 amp. I have included an online manual. Post back if this is the problem.
If the all the fuses look could it could be a safety switch, the one for the PTO or the neutral switch for the transmission. If you go to JDparts you will find diagrams to help locate the switches.
The problem also could be a bad starter relay or starter bypass relay, both of these are located behind the instrument cluster. Again JDparts will give you a diagram.
I also attached a wiring diagram.
I have also include some other URLs you may find of value.
http://manuals.deere.com/omview/OMRE71736_19/
John Deere - Parts Catalog
Fuel cap leaking
- //www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/leakfuelcap.html
Instrument glass fogging up
-//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/instrpanelfog.html
Clutch Slip need for .5 inch free play in clutch
-//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/clutchslip.html
How to determine model year
--//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/modelyear.html
Front End Noise
-//www.deere.com/en_US/ag/servicesupport/tips/augusta/5000/backlash.html