It could be any number of things. Throwing parts at it isn't the answer.
Have you checked the wiring to the fuel solenoid? A broken or chaffed hot wire to the solenoid will definitely cause this sort of problem.
Is the engine cooling fins clear of thrash and buildup?
Trash in the fuel tank can cause this sort of problem. The trash will slosh around until it finds the pickup tube.
If you know your way around electrical wiring, get the wiring diagram, a check light, and multimeter and have at it.
If not, take it back to the dealership that you used before.