If you feel that the fuel pump has failed, then this is the proper way of diagnosing the problem before replacing an item that may not be needed. Starting from the basics, take off the fuel cap and listen closely for the fuel pump to come on as a helper turns on the ignition key. The pump runs for only 2 seconds at a time when the engine is not running. The computer shuts the power off to the pump if it does not see a signal from the crankshaft sensor.
Have the helper turn on the key for 3 seconds and off for 5 seconds and on again a couple of times. If the pump cannot be heard, then replace the cap and lift the hood. Check to see if the fuse to the fuel pump is good. If so, then look to see if fuel is the problem by removing the cap on the Schrader valve on the fuel rail on top of the injectors. Take a small screwdriver and push in on the Schrader to see if fuel comes out in force. If not, hold the Schrader in and have the helper turn the key on. Be ready to release the Schrader if there is fuel pressure, for it will come out fairly steady. If there is no pressure, replace the cap and check the relay. Remove the relay and test the terminals that it was plugged into for power with the key off. There should be one terminal with power. If not, there is a bad wire under the fuse block to the battery; it should have constant power at one terminal.
Take off the air cleaner and hold the throttle plate open with your hand. Spray some carburetor cleaner into the throttle body. Try to start the car for 2 seconds. If it starts, the fuel pump is the problem. If not, the engine should be checked for spark. It could be a sensor or computer-related problem. To be absolutely sure, raise and support the back of the Jeep on jack stands, unless the height allows you to crawl under the back without raising it. Unplug the fuel pump connector at the back of the fuel tank. It will be easy to find and has four wires in the connector. Use a circuit tester and test the harness side for power as your helper turns the key on and off. Remember that there will be power for only 2 seconds, so have your helper cycle the key on and off as you check the terminals, allowing 5 seconds between cycling for the computer to reset. If there is power, the fuel pump took a dump and needs to be replaced. If there is no power, there is an open in the harness to the pump from the fuse block.
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