2002 Lincoln Continental Engine stalls in front of light or

I try to describe the information clearly. The first time I found my car stalled when I put the gear to P (park). Then the car intermittently stalls at low speed (driving in a parking lot) and/or stop in front of light. The idling speed could drop to below 500 rpms and dies. The car is fine when car is in motion (driving condition). I can start the car immediately or just wait 1-3 minutes. The old fuel filter was choked and bad, so I have replaced the fuel filte. I also have replaced idling air control valve (IAC valve), clean the throttle body, but the problem is still there and it occurs more frequently. It is surprising there is no error code (Check engine light never comes on). I am not sure if it is related to throttle position sensor, faulty fuel pump or fuel pump relay, or fuel pressure regulator. Any good comments?