Does the battery hold a charge for at least a little while, or not at all? If you can run the 12V systems without AC power even for a little while, it would suggest a battery issue, or the converter isn't charging the battery properly when on AC. If you charge the battery with an external charger and the same thing happens, it's likely the battery. If you bought this trailer from a dealer, then they should remedy either of these issues.
You may also want to check out this thread if the battery works but seems to discharge faster than you think it should:
Battery gone in 36h, where to start?
If the battery doesn't work at all, with no 12V at all when you remove the AC power, I would be checking fuses and the resettable breaker. The resettable breaker is generally located near the battery. Check the 12V fuses in the converter panel inside the rig.