RE: Battery was hooked up wrong!
I was not a licensed electrician, but I did spend 40 years as an electronic/mechanical service tech. and I have owned and repaired my RVs since 1972. Based on that I would offer a couple of comments.
"The converter is using the National wiring code )as it should because it is producing 115 volts (like house current)."
This is not the case. What your converter does is to take a 120V-AC power supply and convert that to a 12V-DC output. The actual voltage out, if properly adjusted will be about 13.5V so that it will also charge the battery as well as to supply 12V power for things like the lights and the furnace.
You should have 120V supply into the converter and 12V out. The battery on most RVs does use white for the positive side and black fo negative. I would remove the lead from the battery negative terminal first and measure the resistance from that lead to the chassis ground. It should be 0 ohms or nearly that. Then measure from the positive to the negative and that will tell you the state of the battery. That voltage should fall between about 10.5V and 13.6V if the battery is anywere near a good one, All of this I would do with no shore power (120V-AC) connected or the power plug not connected.
The next thing that I would do is to connect the leads to the battery and then connect the RV to shore power. Now measure to see what the voltage reads between the positive and negative posts of the battery. If the converter is working and if it is attempting to charge the RV's battery, that voltabe will be higher than what you read with no negative lead connected. If the battery is fully charged that voltage should be about 13.5V. Too high and it will boil the water out of the battery and too low and it won't charge the batterry. But you will not know the peak voltage until the battery is charged, or by removing the battery from the circuit and measuring across the two leads to the battery. You can also measure that at the output terminals of the converter, but the battery still has to be out of the circuit to get an accurate reading.
With the typical, low pirce converters that most RVs came from the factory, the battery is needed in the circuit while in use as a filter for the poor quality output of the converter, but removing it for just a few minutes to measure should not harm anything.
Be sure that you have the battery terminal conncetions clean and tight. You can use a water & baking soda mix to neutralize any acid in the corossion on the battery terminals. You should also check the liquid level in your battery cells and if it is not up to the slot in each cell, use distilled water to bring it up to the proper level. If this still doesn't help, any battery store can test the battery for you.