The oil is full.

more than likely it is the camshaft position sensor. same thing happened to me last week. cheap and easy fix:U:

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there is probably actually a recall on the CMP sensor on his truck may be able to get it done for free but the ford motor company would put in another one that may hold up a year. get the blue after market sensor from somewhere if you can

We have replaced that and it did not help.

did you check the throttle pedal assy? I know there is a procedure for it somewhere, but I don't know where it is