If you have a bad converter, and no battery charger, then there is no way for your battery to be charged. You'll have a flat battery. You may get some charge if you're hooked up to the tow vehicle, but it will be pretty low.
What voltage does your battery measure at the battery itself?
If you're plugged into shore power, and the converter circuit breaker isn't tripped, and you have no 12v lights, then it's very likely you do indeed have converter issues. I just replaced a WFCO unit a few months ago that created the very problem you're describing.
You need to find the converter, ascertain that it is getting 120v power, and physically check the output of the converter for 12v.
The battery will work fine with a bad converter, but it may be very low on charge because of the above described problem. So you may not have enough voltage to run your pump. Again, check the voltage at the battery with a VOM.