Small Engines (Lawn Mowers, etc.): Battery on Lawn Tractor wont charge, purple wire, chewing gum

Question
The battery on my Lawn Tractor with the Kohler CV22S won't charge.  This has been a problem for I think this whole summer.  While taking a break every 45 minutes or so to drink a beer and charge the battery isn't all bad, it is not as convenient as it should be.  

The battery will charge if I put a charger on it.

I had a hard time determining what the regulator was because I suspected that first.  I believe that it looks about the size of the large pack of chewing gum with fins in the back.  In fact, I am pretty sure that is the regulator.  

My question is "How to I check to see if the voltage regulator is bad?"

It has four wires connected to it.  The black appears to be a ground.  There are 2 white wires that are connected to terminals that are labeled "AC".  There is a blue or maybe purple wire that is also connected.  Perhaps the colors have faded over time.

I have tried to measure VDC or VAC on these terminals with the engine running.  I am not getting anything.  I have tried this with the connector connected and disconnected to the voltage regulator.

So I have to assume that whatever is supplying power to the regulator "isn't".

Is there some sort of definitive test to rule out the voltage regulator at this time?  What voltages should I see on these terminals and will it be AC or DC?  I am assuming that I will see AC somewhere and DC somewhere else.  Can you specifically tell me what to check for?

I have 0.4 ohms between the two white wires (connected to the AC terminals).  Either white wire to ground was "open".

I have about 1/2 hour more moving and I am done for the season.  Then I can take whatever apart and fix it once and for all.  

Thanks for listening.  All terminals are clean, and I have checked for hours for any fuses that may be blown.  

Art

Answer
If you are getting no power to the voltage regulator with the engine running then either your alternator is bad or there is a broken wire from the alternator to the rectifier-regulator.  You should be able to measure an AC voltage on the input side of the rectifier-regulator. If the alternator is in need of replacement I would suggest that you purchase the correct flywheel puller.  The flywheel and starter ring gear can be damaged if they are removed incorrectly.