06 F350 batteries draining

The alt is putting out 14+ volts, but the batteries keep dying. The +post on the drivers side battery keep corroding (daily!!), and the batteries drain whether it is running or not. I keep taking the batteries out and testing/charging them; they are perfectly good. I have removed almost all acc fuses, problem still persists. Have no local dealer to go to.

Help.

I'd run a test light in series between the positive post and the positive cable. Then start pulling fuses until the test light goes out. Then, that's the system that's causing the drain. Batteries could be discharging through the base if they are in a metal box and the cases of the batteries are dirty.