Ford Super Duty (1999-2016) :: Radio Does Not Shut Off When Doors Open

I have a 2004 F-250 SD, Crew Cab, 6.0L diesel. Out of the blue, when opening the door with the key off and out, the dome lights stopped working, the radio wouldn't shut off and I would get no warning that I had left my lights on (nor any other warning coincident with the door opening). Just as if the truck is not detecting the door being opened.

One would immediately suspect the door switches, except that this was a suddenly occurring problem that affected all four doors, by sheer odds, pretty much negating this problem as one to do with the door switches. Still, I did spray the switches with WD40, couldn't hurt, right?

I have replaced relays (#306) with known good relays, I have pulled and looked over every single fuse. I have read of door post wiring issues with F-150's that speak to this issue for that model, but am not convinced that translates to the F-250. I'm at a loss, and almost perfectly convinced this is a computer problem (the GEM, though it's called something different now). But before I go replacing expensive computers, I would like to know how to diagnose this.

As it is, I've learned to live with the fact the radio will stay on when I get out of the truck and will time out after 10-20 minutes. I've learned to live without the dome light coming on and have counted my blessings when the foresight of some engineer saved me from a dead battery by knowing that I would leave the manual dome light switch on from time to time. I've learned to look back at the truck to make sure I haven't left the headlights on. In other words, I've learned to live with this problem.