I'm not sure on a trailer that old if things should come on automatically. My 1986 popup has a switch on the converter that I have to flip to get battery power in the coach.
I would unplug the shore power cord so I was safe. Then I would go read battery voltage at the battery with a meter. Then go into the trailer and disassemble the front of the converter\charger until I saw the wires coming into the DC fuses. Then use the meter to see if I can find battery voltage on the thick wires that feed the 12v fuses.
If you have power there then the wiring is good back to the converter\charger panel and the panel itself is suspect. If you can't find power at the converter\charger panel then you need to find the fuse or circuit breaker out on the tongue that is interrupting the current. It probably wouldn't hurt to check and clean up where the battery negative cable connects to the frame.
.
2001 Suburban 4x4. 6.0L, 4.10 3/4 ton **** 2005 Jayco Jay Flight 27BH **** 1986 Coleman Columbia Popup