I know you said you already checked for broken wires but... did you happen to check in the driver's door boot where the wires go from the chassis to the door? I say that because my '95 ZJ had a broken ground wire in there and would only work the power windows when the door was shut. I don't know too much about the new models but maybe yours has the feature like my TJ where when I open the door it shows me the mileage (digital). Possibly yours turns on the dash cluster lights instead so that you can see the mileage?
The next place I would look if all is well there is somewhere down the line of the switch on your door that activates when you open and close, although I've never encountered a vehicle before that wouldn't let you operate the lock/window switches with the door open.
From ZJ to TJ.