I assume you are talking about 12v power, since the wall outlets, a/c, etc need shore power (120vac). Is the trailer plugged to shore power, or relying on battery only? And does "no power" means nothing at all, i.e. no lights, fridge won't turn on even on LP, water heater won't fire up, etc? Just double-checking because sometimes the problem report isn't 100% complete.
Was it working ok before the new battery was installed? Or is this "new to you" and maybe the problem existed before the new battery went in?
The prime candidates are the battery ground to the frame (negative terminal) and a fuse or breaker inline with the positive cable. From there, do as kcmusa suggests.
Also, can you tell us what power center (12v fuse panel and 120v breakers) is installed? Make & model? That will give us some clues as to how the battery works in conjunction with the 12v electrical system.