I would take the batteries to Autozone or Discount and have them Load tested.
Most likely the converter is trying to charge the batteries and keeping the alarms from going off but once you put a load on the batteries / take them off the converter they act like they are bad.
When was the last time you checked the water level in your batteries?
2011 Rockwood Mini Lite 2306 - Matt
2004 Dodge Ram 1500 Qaud Cab 4x4 with 35" tires and 3.92 gears, Dynatech Longtube Headers & Fabtech 6" lift + Superchips with shift Tuning
Nights Camped 2011 (37) - 2012 (16)-2013 (2) -2014 (5) -2015(0)
USMC 91 - 95 - F/A-18 Aviation Ordnance