Baccus,
It would pay you to ring Graeme @ Engel World, Midland, WA he would be able to advise you on where to go and what to do.
Very knowledgeable, honest & fair fella.
Took my old yellow (25+yo) Engel to him when it developed the symptoms you mention.
First up he told me the complete unit needs to be replaced ($600.00) I told him to go ahead.
When I went to pick it up the bill was $110.00? When I asked him to explain he said it was only a capacitor that had failed, not the unit.
Now you can't get more honest than that, could have slugged me the $600.00 and would have been none the wiser.
Graeme asked me did I run the Engel directly off a generator and took me out to the back of his workshop and showed me evidence of what can and does happen?
He explained that many Engels fail for this reason. Honda even slapped a law suit on him but withdrew it when he proved that even the new inverter type generators "hunt" (revs up & down when running out of fuel) which in turn alters voltage delivery which in turn causes electronics failure.
His parting words were, "Run your Engel on 240v at home off the grid but when you go bush ALWAYS run it only on 12V.
By all means run your genny to charge the battery but have the battery between the genny and the fridge.
Give him a call, he no doubt can explain it better. Ask for Uncle Graeme. (note** He's not my Uncle.)
http://www.yellowpages.com.au/wa/midland/engel-world-13228931-listing.html
Good luck,