So the first thing I would ask is what is the voltage of batteries now. It is not unusual to not be able to charge at completely discharged battery, although I would expect at least one of the three paths you articulated to work.
This would lead me to think possibly a main fuse, generally inverter manufactures like a class T fuse, but some times ANL fuse is used also. Both of these can the large currents of a inverter. In any event it is always difficult to trouble shoot this stuff over the internet, but if your willing to take some pictures and have a voltage meter and take some measurements, we could certainly try to come up with a plan.
I am not aware of any external reset switch for the magnum inverter other than what is on the unit, so I am not sure what you are talking about there. Of course I would say the fact that none of the other devices can charge it, that is a moot point at this moment. Walking you through the setup procedure for magnum could be done, but I don't expect that to be the issue at the moment.
So, what voltage are the batteries at? Can you read that on magnum remote?
Do any 12 volt devices work (lights, fridge)? And I would kindly ask you to take pictures of the electrical area and we can go from there.
If you want feel free to contact me with a PM if you would like.