I have been having a random fuel pump problem, sometimes it will start other times it will just turn over and over. I thought I would change the fuel pump relay to see if that will solve the problem, it least it is the cheapest to start with. Before I start this little project below I tried starting the blazer with no luck. It would just turn over.
I thought the relay is in the glove box closest to the drivers side. With the horn relay in the middle. I tested the horn, works well, the swapped it with the relay closest to the drivers side. Blazer fires up. Good.
So it shut it off and put the old fuel pump relay in the horn location. Horn works. Curious now. Try starting blazer. It is running fine. More curious. I shut it down again and pull out all 3 relays. Try starting blazer expecting it not to run and there it fired up. Totally stumped now, I thought I would move the Blazer to a better location to work on it some more and it would start. UUGGGHHHH.
So my question is where is the relay for the fuel pump?

 

It is the one in the middle. Grab it, turn the key to run, it should click,(turning fuel pump on) then about 2 seconds later it will click again (turning off). That means it is working correctly, and problem is pump, wiring or fuel pressure related.

My blazer used to wanna do this. I would go to start it, it would almost hit then not start, I go to start it again, and it just wants to crank. I would get by this by turning the key to run, then off, then run, then off, to prime the lines a couple times. Then it would fire right up. It turned out to be my leaky *** regulator, I guess dropping or not being able to hold enough pressure. Try flipping the key back and forth a couple times next time you try it.