No power to the fuel pump

Could be the relay or something else.
The relay powers the pump for 3 seconds on crank then the engine computer must see RPM or oil pressure for the relay to keep sending power to the pump.
You could bypass the relay to check the pump operation.
The relay is grounded / controlled by the engine computer.

The oil pressure sensor only keeps the pump running after the vehicle is started. If you turn key to on, the computer should signal to the fuel pump relay, turning the pump on for a couple of seconds to pressurize the fuel system. Then the computer signal stops. When the key is turned to start-cranking the engine- the computer again energizes the fuel pump relay, keeping the pump running until the engine starts.
If you have a voltmeter or test light, pull the relay out and check the relay terminals. One should be hot at all times-the power feed for the pump. The computer signal will be on the coil side of the relay-will have power for 2 or 3 seconds after key is turned to on. Or it will have a constant signal when the engine is cranking. If you can find both hot terminals at the relay, then start looking for a bad wire from relay to pump, or a bad ground for the pump, or a bad ground for the relay's coil side. Post back if unclear or other questions. When you pull the relay out, the diagram for it will be on the side of the relay-telling you which is the power feed and the terminal to the pump, and the coil side of relay, both the coil power side and the coil ground terminal.

Well there is no shutoff relay, but there is a fuel pump relay that powers the pump.
I would check it first. The computer grounds the relay for 3 seconds when you crank the engine to boost fuel pressure. Once the engine starts the pump is powered only if you have oil pressure.

The pump relay is grounded by the computer, for 3 seconds when you crank the engine, and after the computer sees oil pressure or RPM.
If the engine will not start the relay stops providing power after the first 3 seconds.
You would check for the ground signal from the computer - most people either jumper the relay terminals or use another relay as a test.

Generally speaking, its supposed to do that.
The fuel pump(s) is powered by a relay that turns on for 3 seconds when you turn the key on. If the engine does not start and produce oil pressure, thats all the power the pump gets. If you were in a wreck the pump would shut off when the engine dies even with the key on to prevent a fire.
You would need to jumper the relay to make the pump run beyond the 3 second time.

Two things:

First, are you aware that your vehicle will only have power to the fuel pump for about 2 or 3 SECONDS before engine start-up? Then the engine must be running for it to have any power beyond that?

Second, is the "Security" light flashing on your dash? If so, you have a security system problem. There won't be any power to the fuel pump.

Fuel pump power starts at the ECM/Batt fuse in the underwood fuse block. From there it goes the the fuel pump relay and then to the fuel pump. If you pull the fuel pump relay one pin should have power all the time. This is power from the ECM/BATT fuse. Two of the pins should be grounded. The last pin is power from the ECM. it hold have power for 3-5 seconds hen the key Is turned on and anytime the engine is cranking. Find out what is going on at the relay and then we'll have a better idea of what direction to proceed. Let me know if you have any questions and I'll do my best to answer them. Thank you for using FixYa.com!

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The fuel pump is controlled by a fuel pump relay, and the relay is powered by a fusible link attached at the starter positive cable, and there is also an inline fuse between the fusible link and the relay. Check at the fuel pump connector at the fuel tank for current. When the ignition switch is turned on, engine not running, the fuel pump should receive current for about 3 to 5 seconds; then the ignition has to be turned off for about 10 seconds, and when turned to the on position should give power to the fuel pump again for a 3 to 5 second interval. If ther4's no power at the fuel pump connector the problem is either the relay or the wiring between the fusible link and the relay.

The engine computer turns on the fuel pump for 3 seconds when you turn the key to "ON".
If the engine does not start, the pump will not run.
When you turn the key to "Start", the fuel pump runs all the time the key is held in start.
When you turn the key on, it actiavtes the power relay, which provides power to the PCM or engine computer.
The PCM then activates the fuel pump relay, sending power to the fuel pump.
You should have one wire with 12V for 3 seconds in "run" position. This comes from the fuel pump relay to the inertia switch in the trunk and then to the fuel pump.
You should have one ground wire. black
One wire going to the fuel guage.
You may have another ground iwre ging to a diode before going to ground.

I would check the ground for the fuel pump relay that operates the switch side of the relay.
You should have 2 12v inputs to the relay. When the relay gets 12v input, it closes the relay switch on the heavy current side that sends 12v to the fuel pump.

A relay is needed because you don't want heavy current going through the switch.

Also, most cars only run the fuel pump for 2 seconds when the key is turned on because you don't want the fuel pump running without the car running. If you listen closely at the fuel tank, you should hear the pump run for 2 seconds when you turn the key to "ON"
When the key is turned to "START", the fuel pump should run continuously.
The engine computer tells the fuel pump to shut off if the engine rpms are zero.
So, I would check the switch side of the relay. Power amd ground.