Lead-acid batteries can go dead in a number of different ways. When lead-acid batteries are excessively discharged they "sulfate," forming chunky white crystals of lead sulfide on their lead plates. Sometimes the sulfate crystals on one plate touch those on another, forming a bridge that creates an electrical
bridge that shorts the battery out. (This is a shortened explanation.)
Once a battery has been sulfated, it won't retain a charge anymore. (More on this below.) Worse yet, charging a shorted battery can boil the electrolyte, causing it to explode and spatter sulfuric acid all over the place. Very dangerous . . . which is why many battery chargers and converters won't charge a dead battery (or power the lights in your trailer).
One note about sulfated batteries. In most case recovering them is a loosing battle, but special battery-saver systems like a BatteryMinder can restore some of a lightly sulfated battery's capacity.