My husband's 03 1500 is having similar problems (I am no means a car whiz, just trying to help him figure out the problem).

Saturday night he shut the truck off at work, the lights did not go out right away as they are set on a 60 second delay well some idiot that was trying to be helpful and thought he turned out the lights but instead turned on the bed lights, when hubby went to leave work the battery was dead, another guy jumped the battery the truck was running. On his drive home the truck would bog down and the lights would dim as well as the needle on the battery gauge dropping sharply when he was braking or had to come to a complete stop sometimes shutting off however it restarted right away without being jumped. He made it home and parked the truck. I started it yesterday and it started fine so I took it for a 3-4 mile drive having no trouble even while coming to a complete stop (the battery gauge remained solid at one line above 14, see I told you I'm not a car whiz) until I got the truck home and brought it down the driveway and stopped to put it in reverse then it shut off completely with no warning (the battery light came on after it shut off).

We took the truck to the local Auto Zone last night and they tested the alternator and the battery, one guy said it was the battery (with the mobile tester) the next guy said it was the alternator (with the hand held tester) We bought the alternator (the second guy a manager) said he would take the alternator back if it was not the problem (which is something they normally don't do) they also tested the new alternator before we left the store, we went home and put it on, the truck was worse than it was before so we went and got a new battery and put it in, the truck is STILL doing it.

Any ideas? By the way should the alternator be 105 or 145 amp?

 

It could be a fusible link that needs to be replaced or the PCM might need to be checked.