What about the battery fuse's fuse holder? Any corrosion there?
On the DC fuse panel inside, are all wires tight, especially the big battery wire lug set- screws?
Turning on the lights and getting a beep suggests that turning on the lights draws so much battery it makes the voltage low enough to set off the LP alarms low-voltage alarm. It should show red? light as well as beep while it still has any juice left to run those.
That would indicate a major loose connection? --back to that fuse holder? No idea.
Another elimination test is to disconnect the battery with shore power on so the converter only is doing the 12v. This by-passes the whole battery fuse area.
