No power at the fuel pump or injectors

Relay failed? Ignition switch OK (power to relay)?

I want to say check the main relay and it's fuse, but if you can hear the pump running then the relay should be ok.
Maybe check the fuel injectors then.

You don't mention what kind of car it is, but typically, the only time power goes to the fuel pump is when the ignition switch is first turned on and it will run just for a few seconds and then quit. When I replace the fuel pump I will cycle the ignition switch several times, leaving it on for about 5 seconds or so to get fuel to the injectors. This is all controlled by a relay.
Once the vehicle is started it receives signals from the oil pressure to a relay to keep the fuel pump running. This was a safety feature so that the fuel pump would not run in case the ignition was left on or the vehicle was in an accident.

The fuel pump is powered from a relay. That relay is powered by the engine's computer ("ECU"). The relay is necessary to scale the low current control signal from the ECU into a high current switch to operate the fuel pump. The high current circuit will likely contain a fuse. That fuse or the fuel pump relay may be defective.

The fuel pump relay is activated for a few seconds when the ignition is turned on before starting the engine. If everything is working properly, you should be able to hear the fuel pump run for those few seconds before starting the engine. This is so the injectors have adequate fuel pressure before the engine is started.

This should be in the owner's manual. I found the below on autozone.com, their repair help location:
An inertia switch is used as a safety device in the fuel system. The inertia switch is located in the cab, generally under the dashboard on the right side. It is designed to open the fuel pump power circuit in the event of a collision. The switch is reset by pushing each of 2 buttons on the switch simultaneously (some models use switches with only one reset button). The inertia switch should not be reset until the fuel system has been inspected for damage or leaks.
When the ignition switch is ON , it turns the EEC power relay ON . The EEC power relay provides power to the powertrain control module (PCM) and the control side of the fuel pump relay. Power for the fuel pump(s) is supplied through a fuse link or high current fuse attached to the starter solenoid (battery side). From the fuse link or high current fuse, current flows through the fuel pump relay and inertia switch to the fuel pump(s). The fuel pump relay is controlled by the PCM.
When the ignition switch is turned ON , the fuel pump(s) will operate. If the ignition switch is not turned to the START position the PCM will shut the fuel pump(s) OFF after 1 second. The PCM will operate the fuel pump(s) operate the fuel pump(s) when the ignition switch is turn to START position to provide fuel while cranking.
After the engine starts, the PCM will continue to operate the fuel pump(s) unless the engine stops, drops below 120 rpm or the inertia switch is tripped.

Check your main fuel relay.



Fuel Supply System


PGM-FI Main Relay


Description


This PGM-FI main relay is located behind the dashboard


lower cover. The PGM-FI main relay actually contains


two individual relays. One relay is energized whenever


the ignition is on. It supplies battery voltage to the PCM,


power to the fuel injectors, and power for the second


relay. The second relay is energized for 2 seconds when


the ignition is switched on, and when the engine is running.


It supplies power to the fuel pump.


PGM-FI


MAIN RELAY



FUEL


PUMP


RELAY


Relay Testing


NOTE: If the engine starts and continues to run, the PGMFI


main relay is OK.


1. Remove the PGM-FI main relay.


2. Attach the battery positive terminal to the No. 3*


terminal and the battery negative terminal to the


No. 2* terminal of the PGM-FI main relay. Then


check for continuity between the No. 5* terminal and


No. 2 terminal of the PGM-FI main relay.


• If there is continuity, go on to step 3.


• If there is no continuity, replace the relay and


retest.



*: 8P CONNECTOR


To FUEL PUMP


3. Attach the battery positive terminal to the No. 4 terminal


and the battery negative terminal to the No.


7* terminal of the PGM-FI main relay. Then check


that there is continuity between the No. 3 terminal


and No. 1 terminal of the PGM-FI main relay.


• If there is continuity, go on to step 4.


• If there is no continuity, replace the relay and


retest.


4. Attach the battery positive terminal to the No. 1 terminal


and battery negative terminal to the No. 2*


terminal of the PGM-FI main relay. Then check that


there is continuity between the No. 5* terminal and


No. 2 terminal of the PGM-FI main relay.


• If there is continuity, the relay is OK;


If the fuel pump still does not work, go to Harness


Testing on the next page.


• If there is no continuity, replace the relay and


retest.



To PCM CONNECTOR


TERMINAL A4


To ST. SWITCH


To GROUND


To IGN. 1 To BAT


To PCM


CONNECTOR TERMINALS


A13 and B1


FUEL PUMP


RESISTOR


FUEL PUMP

PGM-FI main relay 1 (FI MAIN) is energized whenever the ignition switch is ON (II) to supply battery voltage to the ECM/PCM, power to the injectors, and power for PGM-FI main relay 2 (FUEL PUMP). PGM-FI main relay 2 (FUEL PUMP) is energized to supply power to the fuel pump for 2 seconds when the ignition switch is turned ON (II), and when the engine is cranking or running.

I suspect the at this point, the main relay is defective. This relay controls power to fuel and spark circuits.

The PGM-FI Main Relay is actually comprised of two individual internal relays. When the ignition switch is initially turned ON , the Powertrain Control Module (PCM) supplies ground to the PGM-FI Main Relay. This ground triggers one of the PGM-FI internal relays that sends battery voltage to the fuel pump for two seconds to pressurize the fuel system.
When the engine is running the PCM supplies a continuous ground to the PGM-FI Main Relay. The supplied ground keeps the relay in the "closed" position providing electrical current to the fuel pump, keeping the fuel loop pressurized while the engine runs.
If the engine is not running with the ignition on, the PCM cuts the ground to the PGM-FI Main Relay, causing the relay to "open" and stop the electric current flow to the fuel pump. As mentioned previously, if the engine is not running, the PCM will only supply ground to the PGM-FI Main Relay for two seconds when the ignition switch is initially switched to the ON position.
The PGM-FI Main Relay also supplies electrical power to the Idle Air Control (IAC) Valve and to the fuel injectors.

TESTING


If the engine starts and continues to run, the PGM-FI Main Relay is working and does not need to be replaced.

1. Locate and remove the relay.

On some models of the Civic and Civic del Sol it is located to the left of the steering column under the dash. Many later models position it either near the passenger right side kick panel under the dash or by the driver left side kick panel up under the dash.

1. Attach the battery positive terminal to the No. 2 terminal.
2. And the battery negative terminal to the No. 1 terminal.
3. Check for continuity between terminal No. 5 and 4.
4. If there is no continuity, replace the relay and retest

The neon don't have one, check the fuse and relay's. The fuel pump is also controlled by the Auto Shut down relay (ASD). The power supplied to the fuel pump. Ignition coil, fuel injectors, and parts of the power module is controlled by the logic module through the Automatic Shutdown Relay (ASD). The ASD relay is closed (allowing power to flow through it) when the ignition is first turned on. If the signal from the ignition reference is lost while the engine is running  the logic module cuts power to the ASD, which in turn removes power from the fuel pump, ignition coil, injectors and those parts of the power module.  This causes the engine to shut down. Good luck and hope this helps. 

there is a reset switch in the trunk on the right side under the carpet or in the trunk on the back wall by the tail lights i had same problem found it and it was the fix i have the same car 89 5.0 trunk style hope this helps