1991 GMC Sierra 1991 GMC K2500 Sierra hard to start

I have a 1991 GMC Sierra that is hard to start. It cranks just fine, however, if the engine starts, it dies within 2 seconds. This can be repeated sometimes for 10 minutes. I've tried depressing the accelerator slightly when it does start, thinking that the engine is cold and there's a problem with the idle air intake, however, this does not fix the problem. After a few starts lasting over 5 to 10 seconds, though, the truck will start and idle just fine.

I've replaced the battery (to actually get the truck to crank well, as the other battery barely turned the truck over), and the fuel relay. When I first replaced the fuel relay, I could actually hear the fuel pump kick on when I turned the truck to "on". When I heard the fuel pump pressurize the line, I could get the truck to turn over and idle for a small while (up to a minute), but then it would die eventually. However, most times, I don't hear the fuel pump at all.

While this may be unrelated, when going up a small hill, the truck died. Then engine would crank just fine, but not start. I got a push up to level ground, and the truck turned over and started just fine. Drove the truck to a gas station and was only able to put in 8 gallons of gas.

I plan on taking it to a trusted mechanic for a diagnostic this weekend, but I'd like a second opinion on the matter just so I can be certain I won't be wasting my time with anything.

Thank you for your time.

P.S. When I bought the truck, I was able to get the repair manuals for all systems. However, being completely new to car repair (this truck is going to be a learning tool), I have no clue how to read them. Any pointing in the right direction for a crash course on understanding them would be appreciated.