T 600 start issues.

I have an 06 KW T600, C15 Accert. When you turn the key it tries to turn over then just clicks. Batts are showing 13+ volts on the gauge. All lights ect work. Runns fine and shows 14 volts while running. Had a pull start. Got a used replacment starter just in case. This entire problem started just after I accidently attempted to start it in gear. Didnt notice the dog had bumped the shifter. My fault, I should have pushed in the clutch. Im going to try cleaning and tightening the connections in a few hours as I have a mechanic friend with tools to help me. Worst case we will change out the starter. My question is could it be that it just carboned up one of the connections and isnt getting full voltage? Or if it could be the cylinoid on the starter causung the issues? Also if the motor were bad, I dont see how it could engage and try to turn the engine for about 1/2 a revolution, then start clicking. It acts like a dead batt. Im open to suggestions. I am a rated journey level electrician, and have done many starters before, just not familliar with the setup on this particular application. Had a T/A mechanic try to jump start it and it had no effect at all. He said the starter must be bad and that the cylinoid was sticking. It did seem to pu;; the voltage down really low then hold it there. Rapping on the starter got the voltage to come back up. Im leaning towards a bad cylinoid but will take any advice you may have. Thx.

 

Also can the cylinoid be swaped without droping the starter? Thx.

 

It dosent, if it did it would not have allowed me to attempt to start it in gear causing the issue to begin with. Im thinking of installing one once I get it working again though. Thx for the reply