I've had the same problem, it was the fuel pump.
It was easy for me to diagnose because I have a fuel pressure gauge. It gave out on me at a set of lights one day (only time my car has ever broken down) but at the time I didn't know if the lack of pressure was due to a gubbed pump, injector or fpr.
Pulled the plugs to see if I had a cylnder full of fuel - nope.
Swapped out the reg - still the same.
I did the pump last because it was the biggest pita to do and because I could still hear it prime when I switched on the ignition. It would build a little pressure bit nowhere near what it should and then the pressure would drop away to zero withing a second or 2. Fitted an old pump and she fired right up.
What type of fpr do you have, does it have a spare port to fit a pressure gauge? If so bang one on and rule out the fuel system as the symptoms make me think that will be the prime suspect.