Inside the steering cylinder, the hydraulic ram that moves the tie rods, there is an o-ring, and there should be 2 o-ring "backers", one on each side of the o-ring. Sounds like the o-ring is shot, and the backers are gone.
I had this happen to me on my Fox SPF; I am not sure if your John Deere is similar, but I had the exact same steering issues that you are having.
The repair parts cost $3.00. Took about and hour of my time to replace the o-ring and backers.
Hope that helps! Best of luck!