12 volt not working

Hi guys, have not posted here in several years as I have been working out of country. The trailer also has been sitting, but I have tried to keep it In working order. However I have discovered a problem that maybe you guys can help me with. I seem to be having problems with the electrical system. When plugged into shore power (110v) everything works fine. Unplug from 110 and nothing works (lights, bathroom fan, etc) even though I have installed a brand new battery. If trailer is plugged into truck, everything works fine including tail lights. I have checked electrical panel and everything seems fine, no loose wires or blown fuses.
Has anyone experienced this type of problem. Any ideas to fix this. Thanks for the help. Greg