1999 SAAB 9-3 repair Question Fuel

Engine Performance problem
1999 Saab 9-3 repair Question 4 cyl Front Wheel Drive Automatic

On initial turn of the key in the ignition switch, the fuel pump will run for about 5 seconds and the engine will start and run until that first few seconds of fuel is used up, then the engine will quit. Trying to restart, with the key off and then back to start, will not start the pump again, and of course, neither will the engine run.

I've read somewhere in different forums, that the system will run a pre-pressure pump start then hand the normal setup to some other control - but haven't been able to confirm or find anything else related to the cause.

If the pump was bad, it seems that it wouldn't run at all - or am I mistaken?