I wouldn't let this defer camping - use a battery charger as substitute converter and diagnose/fix later when your not camping. As you probably know - the older series parallax converters don't have the best rep and upgrading to modern smart converter maybe smart regardless.
Not sure why some of the items work and others don't - that would usually imply fuse/loose wiring except that you seem to imply everything works on battery only. At any rate I would start with checking the distribution panel for loose wiring/fuses and check the output of the converter. Some of the older converters require battery to operate and I think your distribution panel is setup so some of the DC power is filtered through the battery (probably the fridge) ... so maybe you don't have an issue.