Assuming you have a 12V battery installed, check ALL connections to it for corrosion, etc. Make sure the battery is properly grounded to the chassis, check the battery itself for fluid level, specific gravity (which would indicate level of charge), main battery cut-off switch - if so equipped, and the battery charger itself. A 12V battery should read about 12.6 volts when fully charged; about 13.5-14.5 volts when the charger is active and charging the battery. You said you checked the 2 main fuses. There may be a fuse panel which contains several more fuses for individual circuits. Check them. Also, you cannot check automotive fuses by just looking at them. You need to check them with an ohmmeter to be sure.
Even if the battery is bad, the converter/charger should power the 12V systems while you are connected to shore power. It sounds to me as though there may be a battery disconect switch and it is switched OFF. Many rigs have them and it shuts off all 12V power.
Otherwise, it sounds like both your battery and converter/chager are either bad or offline. That would be odd, though sometimes the converter/charger is wired through the battery and is affected by corrosion or bad conections there.
Is this a new problem or have the 12V systems never worked since you had the trailer? When did the problem begin?