Lost the transponder part of my broken key and is stuck in anti-theft mode?

I think this is what you need, you will need to replace any broken or damaged parts.

ADDING KEYS (DOMESTIC)

IMPORTANT:
- To initiate, this procedures requires that a learned master key be available.
- A total of 10 master keys or valet keys may be programmed to a single vehicle.
- This procedure adds keys only. The procedure does not erase previously learned keys.
- The keys to be learned must duplicate the mechanical cut of the current key.
- If more than one valet key is to be learned, immediately precede each valet key with a learned master key.

1. With a previously learned master key, turn ON the ignition, with the engine OFF.
2. Turn OFF the ignition and remove the key.
3. Within 10 seconds insert the key to be learned. Turn ON the ignition with the engine OFF. The vehicle has now learned the new key.

PROGRAMMING THEFT DETERRENT SYSTEM COMPONENTS

IMPORTANT:
- When replacing a body control module (BCM) with an GM Service Parts Operation (SPO) replacement part, set up the replacement BCM prior to the 10-Minute Relearn Procedure or the 30-Minute Relearn Procedure. Refer to Body Control Module (BCM) Programming/RPO Configuration in Programming and Setup.
- When replacing a BCM with an GM SPO replacement part, the module will learn the keys immediately. The existing powertrain control module (PCM) must learn the new fuel continue password when you replace the BCM.
- When replacing a PCM with a GM SPO replacement part, the new PCM will learn the incoming fuel enable password immediately after programming and upon receipt of a password message. A PCM which had been installed in another vehicle would have learned the fuel enable password of the other vehicle's BCM. Perform either the 10-Minute Relearn Procedure or the 30-Minute Relearn Procedure to learn the fuel enable password of the current vehicle's BCM.
- When performing either relearn procedure, all previously learned keys will be erased from the BCM memory.
- Additional keys may be learned. Refer to Adding Keys (Domestic).

10-Minute Relearn Procedure
Use this procedure after replacing the following components:
- The PASS-Key III (PK3) keys
- The BCM
- The PCM

1. Connect a scan tool to the vehicle.

IMPORTANT: If replacing a BCM with a GM SPO replacement part, perform the procedure to setup a new BCM prior to the 10-Minute Relearn Procedure. Refer to Diagnostic System Check - Vehicle in Vehicle DTC Information.

2. Turn ON the ignition, with the engine OFF.
3. Insure that all power consuming devices are turned OFF on the vehicle.
4. With a scan tool, select Request Info. Under Service Programming System and follow the scan tool on-screen instructions.
5. Disconnect the scan tool from the vehicle and connect the scan tool to a Techline Terminal with the current Service Programming System (SPS) software.
6. On the Techline Terminal, select Service Programming System and follow the Techline Terminal on-screen instructions.
7. Disconnect the scan tool from the Techline Terminal and re-connect the scan tool to the vehicle.
8. With a master PASS-Key III key, turn ON the ignition with the engine OFF.
9. With a scan tool, select Program ECU under Service Programming System.
10. At this point the scan tool must remain connected for the duration of the 10-Minute Relearn Procedure.
11. Observe the scan tool, after approximately 10 minutes the scan tool will display "Programming Successful, Turn OFF Ignition". The vehicle is now ready to relearn the key information and/or the passwords on the next ignition switch transition from OFF to ON.
12. Turn OFF the ignition and wait 5 seconds.
13. With a master PASS-Key III key, start the vehicle. The BCM has now learned the key transponder information and the PCM has now learned the fuel continue password.
14. Turn OFF the ignition and wait 15 seconds minimum.

IMPORTANT: Perform this step ONLY on vehicles with EXPORT configured BCMs.

15. With a second master PASS-Key III key, start the vehicle. The BCM has now learned the second master PASS-Key III key transponder information

IMPORTANT: Perform this step ONLY on vehicles with EXPORT configured BCMs.

16. With a scan tool, clear any DTCs.

30-Minute Relearn Procedure
Use this procedure after replacing the following components:
- The PASS-Key III (PK3) keys
- The BCM
- The PCM

1. With a master PASS-Key III key, turn ON the ignition, with the engine OFF.

IMPORTANT:
- This procedure is not available on vehicles equipped with option code (Z49).
- If replacing a BCM with an GM SPO replacement part, perform the procedure to setup a new BCM prior to the 30-Minute Relearn Procedure.

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.
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.

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.

6. With a scan tool, clear any DTCs.

Check out the images (below). Please let us know what happens.

You can get an ignition cylinder and theft deterrent (Passkey III) ring from a donor vehicle. The theft deterrent ring (antenna) simply reads the transponder chip in the key and sends the signal to the BCM.

You do not need to replace the BCM or PCM.

Insert the new key into the ignition and turn it to the "ON" position (do not start the engine).

Leave it in the "ON" position for 10 minutes. The security light on the dash should stay on.

After 10 minutes, the security light should go off. Turn the key to "OFF" and then back to "ON" for another 10 minutes.

Repeat the process one more time (three 10-minute cycles in total).
After the third cycle, the security light should stay off, indicating the system has relearned the key.

Start the vehicle to confirm. Let me know how it goes.