2000 Sierra won't start

[aneveu]

Occasionally, my 2000 Sierra would not start. I would turn the key, things would start to turn, RPMs went up, but the engine would not start.
Each time this happened, I'd be able to start it up about an hour later.
I was told that I needed a new fuel pump and had it replaced two weeks ago.
Yesterday morning (in the dark), the truck did not start again just like before, except I notice that I have no interior lights also. Later that day, I have interior lights and it starts just fine.
This morning, the same thing happened. I'm looking under the hood while the driver door is open and the key is in the ignition. While lightly fidgeting with the battery's positive cable, the lights came on and the chimer started making noise.

I drove it staight to the mechanic where we check these and other connections. It appeared that everything was tight since we could not get the dome light to flicker. ( I am assuming at this point that when the truck won't start, the dome light is also not working).

If anyone has any thoughts, please help.