I know that you said the security light is not on, but try the relearn procedure listed below. Instead of waiting for the light to turn off, just time out 10 full minutes in step 2.
1. With a master PASS-Key III key, turn ON the ignition, with the engine OFF.
2. Observe the STARTING DISABLED DUE TO THEFT message on the driver information center (DIC), after approximately 10 minutes the STARTING DISABLED DUE TO THEFT message on the DIC will turn off.
3. Turn OFF the ignition, and wait 5 seconds.
4. Repeat steps 1-3 two more times for a total of 3 cycles or 30 minutes.
Important: The vehicle learns the key transponder information and/or passwords on the ignition switch transition from OFF to CRANK. You must turn the ignition OFF before attempting to start the vehicle.
5. With a master PASS-Key III key, start the vehicle. The vehicle has now learned the key transponder information and the PCM has now learned the fuel continue password.