raguillard, I'd suspect you have a blown inline 30A fuse in your converter (maybe two). If you have the Elixer converter like I have, these fuses are sort of hidden behind and to the side of the easy to access fuses and circuit breaker panel. If at least one of these fuses blow, the battery will not receive a charge when the converter is plugged into shore power. I decided mine blew when I had the refrigerator running on DC and then activated the tongue jack to raise the trailer (with the truck still attached) and with the converter plugged in.
Check these fuses before you go to the trouble of replacing the converter.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew