Yes, your cross-over cable to the DS battery has gone bad and the alternator has overcharged the PS battery. Had this happen to me a few years back, I caught it before it damaged the remaining wiring but it did fry the battery. New cable back then at Napa was something like $100. that plus 2 new batts and was on my way.

 

Phillip's problem looks more complicated than a crossover cable. I don't have a dual battery setup so I have a lot to learn for sure.
It seems like the voltage regulator would protect against this situation unless there is a bad ground or bad connections.
I'm thinking bad connection is at least a contributor because you can see the corrosion bits blown all over the area that failed. Potential scenario is that the alternator was charging at max due to the poor connection at the PS terminal, truck hit a bump and improved the connection then boom.
I second steve's recommendation for new cable and batteries, and add that you should clean all grounding points and terminal connectors. Check alternator output when you re-start the truck.

 

On the cummins setup, the charge from the alternator hits the passenger side battery and via the cross over cable, charges the drivers side battery. The ECM monitors the drivers side battery & its temperature. If the cross over cable is open then the ECM thinks the battery voltage is at 11~12 V and cranks up the output which in turn starts frying the passenger side battery.

Also, if the alt needs to be swapped... there is an upgrade path to get a 220A alt installed if interested... I have been running one (oem alt from 2012 & up Ram 2500/3500 + term block swap) w/o issues for over 2 years now. Others have for far longer.

 

Interesting Steve, so with upgraded alternator do you also upgrade cable/connectors/fuses, or is that not necessary?

 

Nope, grab new alternator, order terminal block, swap it in and install...

(3) 220A alternator update pics... | Dodge Cummins Diesel Forum (cumminsforum.com)

 

After reading all the solutions and researching the problem. I found a video that described my problem totally. First I want to thank everyone of you that assisted me in resolving this problem. I traced the wires to and one went to the alternator, the other two went to a terminal block right below the right side battery box. The terminals were melted at the positive post of the battery. The main cable was not damaged. I took the advice of one of the people in the thread and asked my son to bring his code reader over. He came over this evening and read the code that was thrown. I had already cleaned the battery cables and installed terminals back on the wires that were damaged. When the code was read, it showed referenced dirty battery terminals. After reinstalling all the wires and cranking the truck the gages were working and the check gage light was no longer illuminated. I checked the output of the alternator and the multimeter reflected.13.9 to 14.4 volts when charging. After letting the truck run for 20 minutes. We reran the codes and the charging system code no longer was present. It appears that the battery cable corrosion was the cause of the alternator overcharging and overheating the terminals to the point that they melted. I will continue to monitor the wires for any sign of heat damage and to ensure they remain cool for a while to come. I believe this fixed the problem with the charging system. Thanks again for all your comments and suggestions. Have a good evening everyone.

 

Thanks for the update.