Ariens 926104 Snowblower key switch replacement & wiring diagram

I'm trying to troubleshoot a series of issues on the key switch on this snowblower.   I started working on this unit for my church and don't have a lot of prior history on it.
 
The key switch was working only occasionally it terms of triggering the starter motor.  The motor would start fine on the manual pull rope provided the key was in the "on" position, and the key could also be used to shut the motor off.   I used a Powerprobe to trigger the starter solenoid and was consistently able to get the starter to work, so I thought the key switch had gone bad.  I ordered and installed a new key switch from Jack's (part #53123700).   The starter still does not trigger off the key, and now manual start only works with the key in the "off" position.  Additionally, moving the key  to "on" while the motor is running actually turns it off, and if I turn the key further to "start" it'll keep running.  It certainly appears that something is connected incorrectly.   I didn't think there was more than one way to put the wiring connector on the switch, but as I type this I'm wondering if I put it together wrong.   It would help me a lot if someone could post a wiring diagram of the switch and starter so I can be more targeted in my troubleshooting.
 
Thanks much for the help.