My door locks won't respond to the console button nor will they respond when the engine is started or turned off.
However, if you try to manually lock them, they respond by immediately unlocking, which, I think, is telling me that the problem is not with a fuse.
Yes, the door-lock light is illuminated on the dash.
Anyone had this issue before?

Can you clarify the statement "manually lock them"

a) they all lock / unlock using key in driver's door
b) they all lock / unlock by pulling / pushing the inner door lock knobs.

(a) or (b) or
(a) and (b) ?

Please clarify the "Door-lock light on the dash," while you are at it.
Is that the red warning light normally illuminated when a door is open, not as in "unlocked" but as in physically open as if to facilitate ingress/egress?

I have a 2003 Jag VDP, I am having a similar problem, first time this has ever happened. We had a lot of really wet snow. Last night after cleaning my car I got in stated it and drove off the interior light stayed on and the dash said "Passenger Door Open" I figured I probably didn't sut it completely when I tossed the snow brush in the back seat. When I got home I opened and closed the door still the light said the door was open. I opened and closed all the doors a few times and still the interior light stayed on and the car will not lock. I fought with it in the freezing cold for about a half an hour until I gave up and disconnected the battery. I don't have time to screw with it today but if anyone has suggestions I would be very happy. I can't even figure out where the door switches are maybe one is frozen or has water in it shorting it out. Never had an issue with any of my Jags in winter this is the first.