Small Engines (Lawn Mowers, etc.): Craftsman riding mower wont start, jumper cable, hp kohler

Question
Hi John,
I am at my wits end. I purchased a used Craftsman 14 HP Kohler Engine. Model 917.257552, Engine CV14s, Type 1452
It was supposed to just need a battery. I got the battery, connects were pretty dirty, so cleaned them, put in a new plug, added oil and when trying to start it made a clicking noise. Hmm.  I was told it could be:
-The engine thing at top is stuck, turn it.  It turns.
-The solenoid: So I got a new solenoid, same thing.
-The Fuse: Changed the fuse.
-Carb could be locked. Not sure how to fix that.  Don't know how to take it off. They said the ball float could be stuck. To just give it a whack.?? I would much rather take it off and check the bowl if someone would tell me how.
-May have over filled oil and caused hydraulic lock. To change oil. (haven't done that yet)

Not knowing much about these engines, been doing a lot of reading. I would try the fixes people say, but I don't know where these things are. I have the manual, but it doesn't show you: Here is card and this is how to remove.

I didn't change starter.
When I replaced the solenoid, I was sure it was that, you can hear the loud clicking coming from there. But after changing, same thing. I love that I am learning all this, but I just want it to get me somewhere.
Any idea's, thoughts?
Please answer as-if I haven't a clue. I am a college Prof and can talk and do this computers, but this riding mower is all new to me.
THANK YOU for taking time to help me in any capacity.


Answer
The solenoid is a high voltage switch that connects the battery power
directly to the starter, and make it crank.
A rapidly clicking solenoid makes me think you either have a weak battery, or a poor connection, or both.
  Disconnect the battery terminals and buff them shiny with a wire
brush, and also where the black cable bolts to the frame, then try it again.  If that does not do it, then take a jumper cable, the ones you have for your car, and hook the red cable to the positive post of the battery, and touch the other red one to the terminal on the starter, it should spark some, and the starter should crank, that will let us know what to do next.  So try that and let me know.