The fuel pump really device you are refering to is actually called the CCRM - Constant Control Relay Module that houses the FP Realy, Ac and Fan relays.
Now, the 'new' one you have, is it the right part matching number for your car? It sounds like its the wrong part or its faulty. If the fuel pump is new and you cant hear the fuel pump prime when the key is on the 'On' position, that CCRM is faulty.
Also, check the wiring that runs from the back of the car and along the carpet on the drivers side of the car. Check for shorts ect.
When i replaced mine, this shop tried to sell me the wrong one. He did have the right one i needed though from a wrecked 2.3.
You could try jumping the Fuel Pump by the tank or using a jumper wire and jump the relay by the CCRM.
Hopefully this link will help you - http://www.allfordmustangs.com/forum...rm-pin-out.jpg
I also forgot to mention that you can jump the FP via the DTC connector but you will have to look that up online as i didnt book mark it.