If the fuel pump is original to the car then its most likely bad. There is also a fuel pump relay that could be bad. A quick test. Remove the fuel line from the throttle body. Attach a small 3/8" diam rubber hose. Place the end of the hose in a 1 qt milk carton away from the engine. Turn the ignition key on and leave it on for about 20-30 seconds. Then shut it off. Your should see a small amount of gasoline in the milk jug. If you see NO gasoline then the fuel pump is probably bad.
The fuel pump is replaced by disconnection the hoses, dropping the empty gasoline tank down and replacing the pump inside. Its a process that you will have to look up and learn about.
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" THE BLACK PARALYZER" -87GT 3800SC Series III engine, custom ZZP /Frozen Boost Intercooler setup, 3.4" Pulley, Northstar TB, LS1 MAF, 3" Spintech/Hedman Exhaust, P-log Manifold, Autolite 104's, MSD wires, Custom CAI, 4T65eHD w. custom axles, Champion Radiator, S10 Brake Booster, HP Tuners VCM Suite.
"THE COLUSSUS"
87GT - ALL OUT 3.4L Turbocharged engine, Garrett Hybrid Turbo, MSD ign., modified TH125H
" ON THE LOOSE WITHOUT THE JUICE "