Hey Techie, not attacking you, is just how i am, direct to the point...
When trying to troubleshoot a problem, you want to cover all the basis and check everything that can have anything to do with the problem at hand.
You clearly forgot to cover logic as the first base of all. If the problem persists even on battery, i think it's safe to rule out the DC jack and charger, no? Obviously the problem will most probably be on board.. With luck (based on the pick up/turn off comment) just a bad contact needed to cleaned, or a solder point broken.
Again, not an attack, simple straight forward personality and electronics logic.