[jpk]

Do some research on the Bosch Motronic system and you'll find that the symptoms you're describing are due the DME relay not working correctly. Don't make any assumptions about how it works based on how a Toyota or Ford does; turning on the ignition does not make the fuel pump run.
The DME relay is really two seperate relays in one housing. One side provides power to the DME computer when you turn the ignition on. The other side provides power to the fuel pump when the DME provides the signal to close that coil. One of two conditions must be met before the DME powers the fuel pump; either the engine must be cranking (signal from the ignition switch at pin #4) or the engine must be running at 300rpm or higher (based on the pulse signal from the engine speed sensor reading the teeth on the flywheel).