2004 Mercury Sable Key less Entry

I would suggest that if the doors unlock, and the doors don't have "locking" issues when you put the car into reverse, and the lights inside go out, that you have a broken wire inside the door.

If your not terribly good at wiring in cars, seek professional help. If you are, it's possible to remove the inner door panel, then locate the keypad on the door, and check for continuity in the wires. However, it can be a pain in the butt to get at these wires, as this system was designed to be watertight, and may be more trouble than it's worth to fix.