I would start by checking fuse number 24 - 10 amp if that okay it sounds like you have a problem with the NATS module but to be sure lets try a reset of the system.
I like to remove the negative battery cable at the battery and hold it to the positive cable. This will discharge the system and unload the capacitors which with hard reboot the system. Then reconnect the battery and try the key.
Here is a repair manual, guide on how to reset the system as well. (below)
VEHICLE SECURITY SYSTEM DEACTIVATION
To deactivate the vehicle security system, a door or the trunk lid must be unlocked with the key or key fob. When the key is used to unlock a door, BCM terminal 74 receives signal
from terminal 14 of the main power window and door lock/unlock switch.
When the key is used to unlock the trunk lid, BCM terminal 17 receives a ground signal from terminal 1 of the trunk key cylinder switch (unlock switch).
When the BCM receives either one of these signals or unlock signal from key fob, the vehicle security system is deactivated. (Disarmed phase)
PANIC ALARM OPERATION
Remote keyless entry system may or may not operate vehicle security system (horn and headlamps) as required.
When the remote keyless entry system is triggered, ground is supplied intermittently
from IPDM E/R terminal 53
to headlamp high relay and
to horn relay terminal 2.
The headlamp flashes and the horn sounds intermittently.
The alarm automatically turns off after 30 seconds or when BCM receives any signal from key fob.
Here is the security system wiring so you can see how the system works.
Please let us know what happens.
Images (Click to enlarge)
Thursday, May 10th, 2012 AT 6:02 PM