A 350 isn't going to jump time. If it does, you've got big problems, bud! It sounds like the fuel pump's dead. The relay is on the firewall. It has a random wire with a spade connector hanging off it, if memory serves me. This is the relay bypass terminal. Jump +12v to that and see if you can hear the fuel pump running. If it does, then the relay's probably bad. If it doesn't, then get under the truck with a meter.
The fuel pump connector is along the DS framerail. Two wires. Disconnect that and check for voltage when you've got the relay bypassed. This can be done with the ignition off, BTW, as long as you take the +12v off the battery directly.
If you have voltage at the connector, then plug it up and try again. It may have just been dirty, but more than likely it's the pump. Don't waste the money on a complete sending unit, it won't take you any longer to just change the pump. Unless, of course, your fuel gauge isn't working either. Get the pump, it should come with the o-ring for the sending unit. Also get the little sock filter that goes on the pickup tube. I believe it's sold seperately.
Drop the tank. It's much easier to do if you remove the bumper. Hopefully, you don't have a full tank. With gas prices what they are, I'm sure you're like me and just putting in $20 when you need it! If it's full, syphon off as much as you can. Clean off the crud and find the notches on the retainer ring. You have to unthread that with a punch and a hammer. You should really use a brass punch to avoid any chance of creating sparks. Bad juju, y'know? Once the sending unit's out, the rest of the procedure should be fairly apparent. Installation is the reverse of removal!