As for the dim lights though, 12 volt lights will ALWAYS dim as voltage drops (batteries are discharged). A fully charged battery is usually around `12.6 volts but when running off of your converter, when plugged into 120 volt power it's around 13.5 volts so they are always brighter when plugged in compared to running from the battery. As others mentioned you may have other electrical problems that are preventing your converter from operating so you are running from the battery so lights will be dimmer.
