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Hello, my name is ***** ***** I am a professional here at Justanswer. Thank you for your question and I will assist you with your concern.If you look at the shift selector out at the drivers side (top) of the transmission where the shift cable connects do you see it move when moving the shift through the range of gears?
Okay Rodney, if the shifter is moving the transmission selector through the complete range at the transmission and the transmission is not engaging then the problem has to be an internal problem and not electronic. The computer system on the 2003 Taurus can not command neutral so its not going to be caused by the TRS. Unfortunately your going to need to remove the transmission and do a tear down to determine the cause.