Small Engines (Lawn Mowers, etc.): John Deere STX 30 Suburban Tractor, solonoid, soleniod

Question
I just bought this tractor from a neighbor. I'm having problems starting it. I've just replaced the battery and now have just put a new $140 Kohler Starter and solonoid on (On the advice of the guys at Kohler)

When I turn the key - I can hear and feel the solonoid Clicking, but it won't crank the engine.
I can "hot wire" it by arking a screwdriver on the solonoid, but would rather just turn the key.

Any Ideas?

Thanks in advance  

Answer
 Hello Scott:

 From what you have written, it Sounds like the Soleniod is Not a Good One. New Ones Right Off the Shelf can be Bad. However, Some of these have a Relay that will go Bad. To View a Diagram of this Mower and Better Assist you, I will need the Serial Numbers also. Hope this Helps. Let me know what Happens, Please. Thanks.

 Good Luck

 Respectfully

 John