Before purchasing a relay, you may want to pull the left side and right side covers and examine all the main connectors closely. Look for a clear/white 2 pin connector and make sure the wiring isn't burnt. Check all the wires for any abnormal appearance. If you pull the Fuel pump relay you should have 2 hot wires with key turned on. The other 2 are the wire to feed power to the pump and the ecm control wire. Just don't go jumping wires randomly- you could blow the ecm. Use a digital multimeter.
You might have power to one wire and if you jump power to pump wire- the pump will run, but if you're missing the other 12 volt signal at the relay a new relay won't fix the problem.