First question, what makes you think the battery was hooked up backwards? Second question, a battery reading 12 volts is mostly dead, if you are reading 12 volts, is that with nothing on, no lights or anything? Turn on a couple of lights, and recheck voltage.
Before all this, unplug the trailer from AC voltage. Disconnect one lead of the battery, and don't let it touch any meta, but leave it exposed. Plug trailer in to AC power, check for lights, etc. If none, check voltage at battery cables, (one connected, and one not), looking fore over 13.5 volts. Pay attention to polarity, and make sure you have the right cables on the right post of the battery. Do not go by looks or colors of the wires. (since it's a 99 model, you don't know who has done what).
If no voltage at the battery terminals, then start tracing the wires. One should go to frame ground, pretty quick. The other is the PLUS wire. Most trailers have a breaker on/under the tongue, or maybe under the front edge. It will have a very small reset button one end. May have to reset it. The converter panel, will have fuses and breakers. There should be one, or two large fuses, 30 amp or so, they control the DC of the converter. There may also be a breaker for the converter that has tripped, turn them all off and back on, just to be sure.
Enough for now, waiting on you to report back.
2012 Ford F250 ext. Cab 4x4
2002 Jeep Wrangler Sahara
2008 Yamaha V-Star 650 Classic
2008 Work and Play 18LT