Check the door switch pins. They are black pins on the inside of each door frame. They may be shot, or need adjusting (if even possible). They are a simple post-type switch that is normally open (open causes the light to go on), and when you close the door, the pin gets pushed in and the lights go off.
Try opening one door at a time and pushing them all the way in by hand....one of them is shot or in need of adjustment, and pushing them hard by hand may force them to close.
EDIT: Read ToddZ below...I assumed (wrongly) that there were pins. He said the switches are integrated into the locks (latches), so look there.
TJR