Very confusing! If you have shore power why start the gen? If no shore power and the gen won't start, why do you expect the converter to work?
Meanwhile, just use jumper cables from your truck to start the gen (assuming no shore power) and then see if the converter works.
The batteries may or may not need replacing--they were at 12.7, which is ok just sitting, but then they collapsed under load (gen starting), so how long have they been sitting in the cold with no float charger because no shore power?
Or what is happening there????
