Do you know how old the trailer battery is? If that battery is dead you won't get lights, brake lights, anything even if you're hooked up to the truck. It has to have enough voltage on its own to operate anything on the 12v system even if it's connected.
If it's an old battery it will need to be replaced regardless, so having that checked and/or replaces isn't a bad first step regardless. It seems like its possible they had it plugged in and there was enough charge to show you the lights, but then that was it.
You can check the fuses, those are for the 12v system.
Of course plug into shore power and see if everything works that way. If it does, then you have a 12v issue and I'd suspect the battery first.
