You need to use your voltmeter right on the converter output terminals to determine if it has failed or not.
In my case, the converter was putting out maximum voltage and the battery was draining away while I was plugged in. When I towed, the battery voltage was replaced.
Connect a short piece of wire first to the negative terminal at the converter, then to your jumper cable and then to the negative terminal at the battery. If that makes your lights get suddenly bright inside the rig, it is the negative connection. If not, try the same thing and this time connect to the positive terminal and the positive battery.
In my case, I found the negative heavy wire that connects to the converter terminal strip was loose in it's screw terminal. Two turns with a screwdriver and everything was fine again.