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Hello and welcome to Just answer.com, Super mechanic here. About your vehicle.
That sounds like a bad fuel pump relay.
When the key is first turned "ON," without the engine running, the ECM will turn the fuel pump relay "ON" for two seconds. This builds up the fuel pressure to normal operating pressure. If the engine is not started within two seconds, the ECM will shut the fuel pump "OFF" and wait until ignition reference pulses are present. As soon as the engine is cranked, the ECM turns the relay "ON," which powers the fuel pump.
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