New Battery or Alternator (both)?

[newracer]

Unless the battery has a dead cell drawing down the alternator output, or loose/corroded connection from the alternator to where it connects to charge the battery.

Jump start the truck and remove the battery + cable and see if it dies. And while it is running see if a wench will stick to the back of the alternator from the magnetic field created by the alternator.

It would be the negative cable not the positive. However this is not good thing to do any longer as it could cause damage to many parts of the electrical system.