INSPECTION PROCEDURE 12: No Diagnostic Trouble Codes (Does not Shift): Comment
WARNING: This page is about a different car, the 2005 Dodge Stratus and 2005 Chrysler Sebring. However, it is still accessible from the selected car via links, so may be relevant.
If shifting does not occur while driving and no diagnostic trouble codes are output, a malfunction of the transmission range switch, or PCM may exist.