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You should hear the pump come on with ignition only, not the start position. Have someone put an ear to the gas filler area when you key it to ignition only, again do go all the way to the start position. If no sound, you have a wiring/relay issue or a bad fuel pump. No answer to the problem yet.
If the listener hears it come on, test the fuel pressure at the fuel rail schrader valve. If no fuel pressure, then likely problem is a clogged fuel filter or crimped fuel line.
I own an 85 and have the GM shop manual. It describes the entire process for testing the system. If the 84 is the same as the 85, I can further help you.
You should hear the pump come on with ignition only, not the start position. Have someone put an ear to the gas filler area when you key it to ignition only, again do go all the way to the start position.
Up until you said to try it again turning the key to the start position. Remember, too, that turning the key to the "ON" position only runs the pump for about 2 seconds. To repeat the test the key has to be "OFF" for 10 seconds, or more.
You'll hear the relay click off, then you can key on again.
Fuel pump relay? If the fuel pump relay were on for the 10 seconds or so until the click, the fuel pump would be running for that time. The ECM shuts down the fuel pump relay after about 2 seconds, with the key "ON". With the key "OFF" the fuel pump relay is not energized.