Chevy 2000 1500 5.3
with a voltmeter, turn the ignition on and measure the voltage at the connector...you should definitely have 12 volts...if NOT, we shall have to look in the fusebox for the fuse that drives your fuel pump~
chance that your replacement pump is faulty...apply 12 volts to it or see if there is continuity at the connector~
Check the fuel pump connector, these are a known fault, sometimes you can see a burnt spot on the inside of the connector, if it is bad then replace it, some of the aftermarket pump assemblies come with a new connector, next replace the fuel pump relay, I'm surprised that the parts store didn't recommend that to you, then see if the pump runs, if not then get your volt meter or test light and start tracing down the power circuits for the fuel pump.
Looking for a Used C/K 1500 in your area?
CarGurus has 1,058 nationwide C/K 1500 listings starting at $1,999.
Search Chevrolet C/K 1500 Questions
Chevrolet C/K 1500 Experts