john deere 5200 problems

[JD5210]

Take the diagram I supplied and a volt meter and start checking things.

It is NOT the fuel solenoid, unless you mean starter solenoid. Did have a lawn tractor that the starter solenoid went bad and for awhile tapping a few times on the solenoid (not hitting) it would start.

 

[Coyote machine]

Dead is dead. Doesn't matter why it went dead, it matters that it did and what part/parts caused it to die. Make absolutely sure your ground cable and positive cables are tightly connected to your battery AND the ground to frame is clean and tight.
Then see if the starter solenoid is getting power to it when you turn key to crank position. If your test light or meter isn't lighting up or showing at least 12Volts at the solenoid lead, then you need to find out why.
Post back.