P0513 Cadillac Code - Immobilizer Key Incorrect

The immobilizer system functions are provided by the Body Control Module (BCM) and the Engine Control Module (ECM), as well as any control modules that store and report the environment identifier.
When an ignition key is inserted into the ignition lock cylinder and the ignition is switched ON, the transponder in the key is energized by the immobilizer coil surrounding the ignition lock cylinder. This immobilizer coil is part of the immobilizer control module. The transponder transmits a signal that contains its unique value, which is received by the BCM through the immobilizer coil. The BCM then compares this value to a value stored in memory. The BCM also monitors various control modules to determine if the stored environment identifiers match.
If both the environment identifier and the value received from the transponder match, the BCM will send the prerelease password via serial data to the ECM. If the encrypted code's unique value is incorrect or the environment identifier does not match, the BCM will send the start to disable message to the ECM which will prevent the vehicle starter and fuel pump from operating.
When the ECM receives the BCM prerelease password, the ECM will challenge the password. The ECM sends this challenge to the BCM via serial data. Both the ECM and BCM perform a calculation on this challenge. If the BCM calculated response to the challenge equals the calculation performed by the ECM, the ECM will allow the vehicle to start.
The Diagnostic Trouble Code (DTC) will be set when the calculated response from the BCM does not equal the calculation performed by the ECM.

• Immobilizer Key not programmed to the vehicle
• Faulty Immobilizer Key
• Faulty Body Control Module (BCM)