My 2003 Navigator doors will only unlock with the key on

Sounds like a vehicle security module problem , but , without doing some testing that would be just a guess .
Checking for DTC'S - diagnostic trouble codes first ,then checking power an grounds to the module . Viewing wiring diagrams an testing electrical circuits for the locks too see if anything is wrong , missing power or grounds etc... Do you know what a wiring diagram is ? How to use a DVOM - digital volt ohm meter to test electrical circuits ? Free wiring diagrams here http://www.bbbind.com/free-tsb Enter vehicle info. year , make , model an engine size. Under system click on body & accessories ,then under subsystem click on power locks . Click the search button then the blue link . If not familiar with automotive electronics your best bet mite be to take it to a qualified repair shop.

Power Lock
The power lock/unlock feature requests all of the vehicle doors, including the liftgate, be locked or unlocked upon a customer request from any interior door lock switch in the vehicle. The power door locking system functions independently of ignition status or vehicle speed. When the vehicle security module receives an unlock/lock command from any door lock control switch, the vehicle security module will activate relays internal to the module to supply the correct power and grounds for the door lock actuators.

Power Unlock Inhibit
NOTE: This feature is not enabled when the vehicle is delivered to the customer. If the customer requests this feature the module can be configured to enable this feature.
With the key in OFF, 20 seconds after electrically locked (remote transmitter, keypad, door lock control switch locked with door ajar) and all doors are closed, the door unlock switch will be inhibited if this feature is enabled. (The lock function will still operate.)
Deactivating/Activating Power Door Unlock Switch Inhibit
NOTE: The power door unlock switch inhibit feature needs to be enabled to perform this procedure.
This is customer configurable. Steps one through three must be completed within 30 seconds.

1. Turn the key to ON, then press UNLOCK three times.

1. Turn the key to OFF, then press UNLOCK three times.

1. Turn the key to ON, within five seconds press LOCK two times.

The user should receive two horn chirps to indicate the system has been disabled or two chirps followed by a horn honk to indicate the system has been enabled.
Pressing LOCK two times again will toggle the door lock control switch inhibit feature state.
Turn the key to OFF to exit programming mode.
This feature can also be enabled/disabled using a diagnostic tool.
Auto-lock Enable/Disable - Using the Ignition Switch
Another way to turn the auto-lock feature off/on is by following this series of steps:

1. Close all doors.

1. Confirm that the key is in the OFF position.

1. Turn the key from OFF to ON.

1. NOTE: Steps 4 through 8 must be carried out within 30 seconds. Press UNLOCK three times.

1. Turn the key from ON to OFF.

1. Press UNLOCK three times.

1. Turn the key from OFF to ON.

1. Verify that the horn chirps. This indicates the enable/disable mode and now is ready to accept program changes.

1. Press UNLOCK once to command the vehicle security module to toggle the auto-lock/relock feature OFF.

1. Press LOCK once to enter the command.

1. Verify that the horn chirps one time. There should only be one chirp indicating that the auto-lock/relock feature has been disabled. If one chirp is heard followed by a longer sound of the horn, the auto-lock/relock feature has just been enabled. Return to Step 10.

1. Turn the key to the OFF position to exit the enable/disable mode.

1. Exit the vehicle and verify that the horn chirps once to indicate that a feature has been changed and that auto-lock/relock has been disabled.