I agree with the other posters that it appears to be a loss of rest pressure on the fuel rail.

You said you hear the pumps runs when you first turn on the key.
Try turning the key to the first position, to make that happen several times, first thing in the mornings.

This will help fill the rail up before you crank the engine. If it starts up thus will help confirm their speculations.

Do it for a few mornings the same way. If it works then suspect a fuel leakage or the other half of the fuel pump relay is not working correctly to turn on the injectors circuit every time.


Some other things that can happen at anytime, as warning signs.

FPR's are notorious for leakage back to the fuel tank or into the intake manifold.

There is also the in-tank pump that has a rubber connecting hose.

Have you notice if it more likely to start hard when under a half a tank of gas?
Or cutting out while pulling up short steep grades?
That points more towards a bad tank pump hose.

Keep listening and looking as the car speaks in a quiet but subtle language!

Phil