2001 Taurus SEL Stalls while idling and at speed

My 2001 Taurus recently started stalling. It does it either while sitting at idle or driving at speed. After it stalls, one of two things happen:

1. The starter doesn't crank when I turn the key and I can hear a high pitched whirring sound coming from the rear of the car. (I think it might be the fuel pump)

2. The engine cranks but won't start, and after a couple of tries the symptoms described in number 1 kick in.

After 1 to 2 minutes, it starts and seems to run fine for anywhere from 30 seconds to a half a day.

I also noticed that it occurs more often when I have my headlights or defrost on, however it has happend with nothing on also.

One time when it happened at a stoplight I reved the engine while waiting for the light to change. I noticed that at higher rpms it started missing and running real rough. Slower rpms it seemed to be fine.

Don't know if it's a sensor, the computer, the fuel pump or possibly a loose wire somewhere. Any deas?:uhoh:

Almost sounds like a fuel delivery problem. Maybe clogged fuel filter?

How many miles on the car?

It just turned 37000 miles. Took it in and had it tested and it didn't have any fault codes. I'll try changing the filter and see it it helps.

Check the fuel pressure before the filter
Check the fuel pressure after the filter
Check the fuel pressure at the engine
Check the sparks plugs and coil packs

check the fuel pump relay. My 01 sel did exactly the same thing. relay fixed it.