Let’s clean up some of the terminology. The Dimensions WIN-12X is an Inverter/Charger. It’s not a Converter or Converter/Inverter.
It does convert 110v AC into 12vdc but only to charge your house batteries, not to run your lights and other 12vdc loads.
So, as Richard has suggested, it sounds like you have one or more bad house batteries.
See, a Converter takes 110vac and converts it to 12vdc to power the lights and other 12vdc loads. AND it charges your batteries.
However, in this setup your batteries power all 12vdc loads and the Inverter/Charger charges those batteries.
An RV with a Converter still powers the lights etc even if the batteries are dead. But an RV with an inverter/charger always relies on the batteries for 12vdc loads.
I agree that you should start with testing the batteries first. This doesn’t mean the problem is not your WIN-12X Series Inverter. That very well could be the cause of your dead batteries in the first place.
We’ve had a number of folks visit here to complain that their early 2000s Dimensions Inverter Charger’s charging circuits have failed and that they’ve found that the company was sold and the unit was not repairable.
Inverters have come a long way since 2005 and you should just find a new 12v 2000w inverter charger with AC Passthrough from another company. Dimensions was sold and is now Magnum. Their MS-2012 inverter is a current day interpretation of your existing device. But there are are other popular choices, too. Xantrex and Victron are two of the more popular modern choices.
So check your batteries and also check your Dimensions inverter’s charging functions.