Cappy is right. When installed in the Intrepid and its LH body siblings, the 2.7L had serious sludging problems, apparently due to a design flaw in the oil drains. They didn’t work properly when the engine was mounted longitudinally (as in the LH bodies); the sludge problem rarely occurred in the cars with this engine mounted transversely (in the so-called “Cloud cars”: Dodge Stratus, Chrysler Cirrus, Plymouth Breeze, and their replacements).
Bottom line: You need to find out the actual oil pressure. I have a feeling the light is indicating an actual oil pressure problem, and the engine is in bad shape.
If you want to keep the car, the best solution is swapping the 2.7L for a rebuilt 3.5L. This problem is so common that there are kits available to do this swap.