Are you certain there is power OUT of the relay?
There should be a fuel pump prime terminal by the fuel pump relay, it will be a red wire with a connector on th end of it. With the key in the crank position, it should have power. No power, the relay is not activating.
Have you tried priming with fuel through the throttle body to see if it will start and stay running?
If it will, then it is certain the relay is bad, as the fuel pump circuit uses the relay to energize the pump until oil pressure comes up, then the signal to the pump comes from the oil pressure sensor once oil pressure builds.