"I'm getting tired of shorting it out across the starter to get it going."  Jeff, what are you shorting across to get it going?  Assuming a 4230 is about the same as a 4430/4630, the contact to spin the starter should only be made when the solenoid/pinion gear is engaged into the ring gear.  If the solenoid was not properly latched to the fork that engages the pinion gear, the starter would spin but "shorting it" would not get it going.  I sounds like you may have an open circuit on one side of the solenoid energizing circuit but that does not explain the starter spinning without solenoid contact.  

 My 4630 wouldn't start today; bypassing the solenoid contact would cause the starter to spin but the solenoid would not energize by "shorting" it to the + terminal.  One terminal for energizing the solenoid is connected to the ignition/key wire and a wire that leads to a seperate terminal on the starter.  The other solenoid energizing terminal is connected to the main solenoid to starter strap.  Once I took off the solenoid cap I saw that this solenoid wire had came "unsoldered" from it's terminal bolt.  I resoldered it and was back in business.  I hope this helps.