I'm not sure about our trucks, but I was working on a Jeep Grand Cherokee with a short that blew the ASD (auto shut down) fuse and it would not crank at all. It controlled power to about 10 different circuits, and they were right when they named it - it automatically shuts down. I suspect it is similar in the Dodge trucks, so hard starting wouldn't indicate the ASD relay to me. If it is still doing it, try swapping one of the relays next to the ASD relay to confirm - make sure they are the same part #.
The fuel shutoff relay sounds like reference to a Brand F maybe? If you've already looked in the manual and couldn't find it, then it probably doesn't exist - at least by that name. A lot of Brand F's had an impact sensitive shutoff to cut fuel flow in an accident. If you thumped the body in the right place with your hand you could trip the sensor and the truck would not start (not funny to the truck owner).
Hope you find the problem with yours.