You said that it dies slowly? That would point towards fuel. (i didn't read the 1st post carefully) You might try and see if the fuel pump comes on when you move the flap on the AFM (air flow meter) If it does not come this suggests that the wiring,AFM or dual relay is bad. I'm going by memory but I believe that when cranking the fuel pump runs off the starter signal. When the car starts the points in the AFM connect and that runs the relay to power the pump.
So... if the AFM is stuck closed or the connector has some wires that are pushed out it will not run. Also pull the rubber boot off of the backside (harness)of the connector and make sure that the pins are not pushed out.
Paul