[wingnut60]

Boonie,
If she is going to continue without a 120volt power source, she needs 2 matched batteries, best if they are deep-cycle 6volts in series hookup. Charged batteries will last much longer in this scenario.
The jack is usually wired direct to the battery--it should work no matter what if the battery is good. If the jack is working, there is a wiring problem, possibly a ground wire that is corroded--these type of elec probs are frustrating to find. Remember, the converter does nothing for the system if not connected to 120volt.
I will guess that if she continues this style of living, the single battery setup is not going to be satisfactory. Also, remember there should be a smoke detector, and possibly a CO detector, and maybe a propane gas detector that will constantly draw on the battery whether she is there or not. How about a radio that has instant on? I'm am not familiar with the model/brand, so don't know how they came equipped that far back.
Another solution is a 2nd battery that you bring out daily or as often as needed and exchange them, taking the down one in to charge--but this charge/discharge will quickly shorten the life of any battery.
Hey, wish you some good luck.