even if the truck and the trailer are set up with a batt + wire, this doesnt mean either plug has been wired with them so that they can be connected.
and even when they are connected, very few amps can make it to the trailer battery, so it will take a very looong time to charge the battery that way.
Im assuming you have a dual purpose 12v battery in the trailer, and these will supply voltage but when they run out of juice they die quickly.... and when they are dead, it takes a LOT of juice to get them back to full charge.
the onboard multistage charger will deliver more amps to the battery and controlled better so that the battery charges as fast as physically possible.... where the truck can only give it a single stage trickle charge thru its batt+ wire and alternator system....
you are correct that the trailer battery may need to be replaced, but still, if you are attempting to charge it only from the truck, a new battery will soon go bad because of the extremely inefficient charging that the battery is constantly being abused with...
a good charging system, and true deep cycle batteries installed, being used PROPERLY, should last a minimum of 6 years with an expected life of 8+ years.
with the truck running and all switches off, you should find a batt hot wire at the trailer plug receptical on the bumper... if not, you may have a blown fuse in the truck.. or maybe it was never connected.
if you DO have a hot wire at the trailer plug, connect a multimeter to the battery and see the voltage.... when you plug the trailer in the voltage should increase at least 1 volt immediately. if not wait a couple minutes to see if the voltage at the trailer battery increases... if no increase, you have a wiring issue in the trailer circuit..... either at the plug (most likely), or elsewhere in the harness. the second most likely place would be where the batt+ wire from the harness connects to the trailer... fuse panel?