I have a D600. I have Dell's recharger.
My experience has been that the battery will not recharge from the power port while in use. If I use the battery and let it run down and then plug in to the power port, the batteries are not getting sufficient juice to recharge (just had this ZRH-DFW over 12 hours). While the computer will work, the batteries are getting nothing.
I do not recall if the battery loses life over time if plugged in right away. I will have to try the suggestion of disconnecting the battery too.
And why don't they have power ports on the AB at row 27?