Repair by replacement might get you there eventually but a systematic diagnosis of the systems will take you to the issue more directly.
Since the batteries and converter are now new you can probably check those off the list. Batteries can only supply the power they've been charged with so the first check is to see if the power from the (working) converter is making it to the (working) batteries. Use a voltmeter and you will see the charging voltage present at each, nominally 14.4V.
Next question is to figure out what's discharging them. It could be something unexpected like a failed electronic assembly or switching control, or something simple like a light being left on in a basement compartment you don't see. Pulling fuses and observing the the current change going out of the batteries will help isolate where the power is going.
Mark B.
Albuquerque, NM