Fuel pump.........as mentioned, it is building enough pressure with the ignition cycle to start it, but isn't putting out enough volume to keep it running. You might bang on the bottom of the fuel tank, sometimes that will give them a little "jump" where they will work briefly (not always, though).
It is not too tough to change, you can either loosen the straps and drop the tank, or loosen the bed bolts and jack up that side of the bed to access from the top. If you jack up the bed, be sure you put some wood blocks or something in there to support it while you are working, it would suck if it fell and pinned you between the bed and frame.