Consider replacing the fuel pump relay first. I have a fuel pump failing in the E36, it has been acting up the last few times the car has been out, but it didn't just die completely. It starts cold no problem then begins to hesitate when warm. If I turn the car off and then back on when its warm it can take two or three long attempts to get it to start.
Its a much cheaper fix (~25 bucks for E36) than replacing the whole pump. I'd hate to replace the pump only to find it was the relay all along.