The DME is the Bosch Motronic engine management computer. It's located on the roof of the glovebox - silver box.
I'm not sure if there is a secondary fuel pump, some cars have them. I just remember reading about as I was searching for a solution to a problem.
It's definitely possible. It could even be the gas itself. You may have to drain it and refill. Get a pressure gauge, pull the regulator and see what kind of pressure you're getting at the fuel rail. A gimpy test would be to pull off the return line on the fuel tank and crank the motor, or even jump the fuel pump if you know how. Eventually it should overwhelm the regulator and you should see fuel returning to the tank...