Assuming your '01 is similar to my '98, the PCM is responsible for telling the relay to close (according to my wiring diagram, it is pin D1 at the PCM). The next step working backwards would be to check the connection between the PCM and the relay and to check if the PCM is sending the signal to the relay to close.

Working back far enough, the ignition switch is a possibility. Most likely it would be a fault that is blocking power to the PCM. If the PCM doesn't have power, it can't send a signal to the fuel pump relay to close. It also won't be able to tell the injectors to fire and so on. If the PCM is not sending a signal to the fuel pump relay, I would probably check PCM power next.