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If you apply throttle can you keep it running? If so then clean the throttle body and MAF sensor, remove both battery cables, hold them together for one minute, then retest. If it still occurs but you can keep it running with throttle then replace the IAC valve.
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Thanks for the new details. Did it appear it only runs with the key in the start position and dies when you let go of the key?
The PATS system would not even allow it to start and it can not shut down a running engine. If there is a PATS issue with the key in the run position, the theft light will be blinking rapid, is that what you see?
The theft system shuts down the fuel injectors or the fuel pump on this model, can you check the fuel pressure with the key on?
To cure the theft light, a Ford IDS or equivalent tool will be needed.
That would be the transceiver near where the key goes in, which reads the code inside the key.