Third post probably has it correct. The 12 volt from the truck usually connects to the load side of the breaker on the tongue of the trailer. If that fuse is open you will have power when connected to the truck and when plugged in to a.
Battery will have two wires on positive, one for break away switch and a heavier one to the fuse. Look for something with two terminals and a rubber cover on the trailer tongue. If you can use a volt meter it is easy to spot.
Less likely, but possible, is you are missing a connection to the new battery. Do you have a heavier wire near the battery disconnected?