Small Engines (Lawn Mowers, etc.): Riding Mower starter keeps going, sears craftsman, key switch

Question
I have a Sears Craftsman 12 hp 38" deck model 917.254640 it started out where it would click but nothing. Replaced the battery and solenoid with new ones and when I turn the ignition key to on position it starts cranking and the starter keeps going even when engine starts. So I replaced the ingnition key switch and same problem.

Any ideas of what else would cause this?

Answer
Hi Chris,

I suspect incorrect solenoid connections at the key switch.  The power to the solenoid's small terminal should only have power when the key is turned to the start position.  Find the key switch terminal that does this.

Let me know how you make out.
Michael