Check battery voltage with battery disconnected, it should be no less then 12.7V. Connect the battery and check the voltage again. If voltage drops more than .2V then you have a draw on the system. If your voltage is 12.5 or more, start engine and checking at the battery bring up the RPM's to about 1800 or until clutch starts to grab. You should read 13.8 volts or more depending on the state of battery charge. The small battery will not cause it not to charge if it is indeed a 12V battery and not a 6V. You may want to check that it is a 12V battery. Also I have seen it many times before where the battery polarity was backwards, this will fry the stator if done.
Check it in the manor I have told you and post your results then we can go from there.
TOM
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