It does sound like you have a charging problem, but before you spend the money on that new converter, check the charging voltage with a meter at the batteries to insure you are, or are not getting that 14 volts there. If you checked the charger and it is generating 14.3 volts...
This link is pretty good:
http://www.ehow.com/how_7663515_test...r-charger.html
Good luck and let us know.