An oil pumping system to carry oil from an oil sump in a pump housing to an internal oil reservoir in another portion of the pump housing. A top plate is attached to a pump rod and moves in accordance with a reciprocating motion of the pump rod. A bottom plate is below the top plate. A pump mechanism, disposed between the top plate and bottom plate, includes a valve seat that contacts the bottom plate, and an upper portion that contacts the top plate. A first biasing element is configured to urge the valve seat upward away from the bottom plate. A second biasing element is configured to urge the plunger upward away from the valve seat. Upward movement of the pump rod allows oil to flow into the pump mechanism. Downward movement of the pump rod causes the bottom of the valve seat to seal against the bottom plate.