The starter will not engage. The problem started with a clicking noise when trying to start. After several attempts the starter would engage and motor would start. Kept gradually getting worse and at this point won't engage at all. I removed the starter and brought it to a John Deere dealer to be checked out. They said the starter was fine but suggested installing a AM107421 Improvement stater solenoid wiring harness as I did. Still no success... Any suggestions ?

Hi,
Usually that kit does it; called a Low Voltage Kit by most Deere mechanics. Check the grounds engine to frame; sounds as if there is not a good eletrical connection somewhere. That starter has a shift-solenoid (moves the pinion and makes the stater spin both) mounted to the side of the starter that can be replaced separately and it can be it though it is a rare occurrence.
Peace,
Clarke