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try the sending unit. Mopar sending units go bad all the time. I have replaced many 3.7 sending units in Liberty's and Rams. They usually get gummed up inside and cannot read when the oil pressure is low at idle, but when the pressure rises from acceleration, it is able to push past the sludge and give a reading. It is a fairly easy replacement on the 3.7, and should not cost more than 180 dollars if done at a shop. (part around fifty dollars, no more than one hour labor) 

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