The only things that should be running directly from the 110 power are your AC, fridge, power outlets, and your converter. Your converter takes the 110 power in and uses it to run its internal battery charger which keeps your 12v
batteries charged. Everything else runs off of the 12v
batteries. Your batteries could be new, but if they do not have a full (or nearly full) charge, and you turn on everything that runs off the 12v
system to test it all at the same time, your batteries may not have sufficient charge to run it all. That could cause the lights to dim and/or the radio to quit. Check your systems monitor to see if it's registering low remaining power in your batteries. If so, you just need to charge your batteries fully and/or turn some stuff off. You can also test each of the lights one at a time.