This can be from a faulty BCM which is common in these cars.
Here is some information from the book:
The body control module (BCM), produces the theft deterrent crank relay and fuel enable signal when ignition is ON and the proper ignition code voltage value is detected. The powertrain control module (PCM) monitors the fuel enable signal during crank. If the proper signal is present on the class 2 serial data circuit, the PCM enables the fuel delivery in order to allow the engine to start. If the PCM determines that the fuel enable signal is not present or incorrect while the engine is running, DTC P1626 is set. The engine continues to start and run as long as DTC P1626 is stored. If the problem affects inputs to the Vehicle Theft Deterrent System (VTD) signal, the starter motor may be disabled.
Conditions for Running the DTC
The engine is running.
Conditions for Setting the DTC
The PCM has detected a loss of the state of health serial data message from the theft deterrent system.
Action Taken When the DTC Sets
The PCM will not illuminate the malfunction indicator lamp (MIL).
The PCM will store conditions which were present when the DTC set as failure records data only. This information will not be stored as freeze frame data.
Conditions for Clearing the DTC
A history DTC will clear after 40 consecutive warm-up cycles have occurred without a malfunction.
The DTC can be cleared by using a scan tool.
Try to disconnect the battery for ten minutes and then reconnect it to see what happens it could reset. If the problem then returns the BCM is bad here is its location you will need a shop to program it for you. (Below)
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Saturday, November 3rd, 2012 AT 2:31 AM