Small Engines (Lawn Mowers, etc.): John Deere 445 no voltage to starter solenoid, john deere 445, starter solenoid

Question
My friend has a john deere model 445 garden tractor with Kawasaki motor.  He had a low battery and put a charger on it for 12 hours hooked up backwards.  Now there is no voltage to the starter solenoid.  I have tested all fuses, OK.  Have tested the fuseable links OK,  Can run hot wire to solenoid from battery and will start, but begins flooding after a minute.  Appears to be a solenoid on the carb and butterfly is only partly open.  Guess the carb solenoid is somehow tied to starting sequence since there is no choke.  Guessing that one of the relays on the board on right side of console is bad, but not sure which one and haven't got time to trace wiring.  Any help appreciated.  Last week found the complete technical manual for this tractor, booked marked it and next day message said file corrupted, good old John Deere.  Any guidance appreciated, John Deere parts catalog not much help

Answer
Gary
Depending on the battery Charger most ones if you hook them up backwards will not charge or burn out the battery, since you started the engine by jumping the solenoid lets me know that the battery may still be good. The first thing I would bring the battery to a place to have it tested you may have a bad cell causing a low voltage. The fuel solenoid needs 12 VDC to completely open and close.When you turn the key the fuel solenoid will open up,you should hear a click when you turn the key to on, don't try to start just turn the key to see if you hear the click if not the fuel solenoid may be bad but make sure your battery is good first before you do any electrical trouble shooting.