Should I hear the fuel pump running with the key on ?
Yes, if you got a good ear. It is common to hear the fuel pump running without the engine. The running sound should come from directly over the fuel tank like it's almost underneath the rear sear.
If it is abnormally noisy, ie you can hear it over the engine running, I suggest you install a new fuel pump. This one is probably headed for a failure soon in that case.
Regards,
Doug
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