I think you have the GM PassLock system? Having a new key or disconnecting the battery disconnects the links between the key and the ECM. This explains how it works, to give you the background for fixing it.
https://www.fixya.com/cars/r29887709-gm_passlock_security_system
To reprogram PASSLock I ignition lock:
Step 1. After replacing the lock, try to start the vehicle with a correctly cut key. There is a one in 10 chance that the car will start.
Step 2. If the new lock does not match the electronic value in the vehicle's computer, an indicator light on the instrument panel will begin flashing and the car will be disabled.
Step 3. Leave ignition in the ON or RUN position.
Step 4. After approximately 10 minutes, the light will stop flashing and remain ON. The onboard computer has then been programmed to accept the new lock's signal. The car can be started.
If the indicator light turns off, the vehicle is probably equipped with a PASSLock II system. Continue with the following programming procedure.
To reprogram PASSLock II ignition lock:
Step 1. After replacing the lock, try to start the vehicle with a correctly cut key. There is a one-in-10 chance that the car will start.
Step 2. If the new lock does not match the electronic value in the vehicle's computer, an indicator light on the instrument panel will begin flashing and the car will be disabled.
Step 3. Leave ignition in the ON or RUN position.
Step 4. After approximately 10 minutes, the light will stop flashing and turn OFF.
Step 5. Turn the ignition on and back to the ON or RUN position.
Step 6. After approximately 10 minutes, the light will stop flashing and turn OFF.
Step 7. Turn the ignition on and back to the ON or RUN position.
Step 8. After approximately 10 minutes, the light will stop flashing and remain ON. The onboard computer has then been programmed to accept the new lock's signal. The vehicle can now be started.
Occasionally, a PASSLock-equipped vehicle will have problems starting. The following information can help to determine the cause of the problem.
The PASSLock system does not disable the starter; it only disables the fuel after the engine has started. If the vehicle will not crank, PASSLock cannot cause this condition. If the vehicle starts, but stalls quickly, this condition can possibly be related to PASSLock.
Most PASSLock-equipped vehicles have a telltale indicator in the instrument panel. When a PASSLock-equipped vehicle is being started, the instrument panel warning light for PASSLock remains on until the engine starts. For this reason a "No Start" condition should not be confused with PASSLock System fault.
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