My first guess is a faulty drive relay or fault in the signal to the drive relay.
The drive relay is supposed to get a tachymetric signal from the coil to know the engine is running. It then powers on the fuel pumps. There is a bypass circuit to power on the pumps during cranking. My guess is the fuel pumps are powered on by the bypass circuit but not the drive relay.
There are other things to check - like the two flywheel sensors. More info is in the L-jet diagnosis page - see the link in my signature.
The drive relay is supposed to get a tachymetric signal from the coil to know the engine is running. It then powers on the fuel pumps. There is a bypass circuit to power on the pumps during cranking. My guess is the fuel pumps are powered on by the bypass circuit but not the drive relay.
There are other things to check - like the two flywheel sensors. More info is in the L-jet diagnosis page - see the link in my signature.