As Forest Gump would say stupid is as stupid does.
Your truck does not have a conventional fuel supply pump like a gas motor does. The injection pump pulls the fuel from the tank under vaccuum.
That being said, try taking the fuel cap off of the fuel tank and leave it off, pump the primer and start the engine. If it continues to run and does not die like it did before. You need a new fuel cap. Now that may sound stupid, but if the vent in the cap isn't working it will now let air flow into the tank as the pump pulls fuel out of the tank and it will not run without that fuel.
Good Luck. Let us know if that worked.
02 2500HD LT D/A SB CC 4X4 BLACK, Westin stainless nerf bars, BW GN Hitch,Racor 60S post oem fuel filter, Oil Guard bypass engine oil Filter. All synthetic fluids. Kennedy boost valve, edge, Modified air intake,EGT & Boost digital gauge,TransferFlow combo fuel & tool box, Air Lift Suspesion Bags Rear & compressor with remote, Bilsteins front & rear, Frontier front replacement bumper.