All the converter does is convert the 115vac to 12vdc. It charges the battery and supplies the 12v power for the lights and other 12v things. It does nothing for the 115v other than using the 115v.
What you have to do is check the voltage coming out of the breakers and if that is good, follow the wiring and see where the voltage changes. If the outlets are powered by the GFCI, check to see if the voltage, both in and out of the GFCI is ok. Does your coffee pot work if plugged into the GFCI? You can try a lamp instead.