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Relay, on top of fuel tank under parcel shelf, check its getting power, if not its fuse, if it is, bin it get a new one.

If you have checked fuel pressure with a gauge and the pressure is normal, are you getting spark to the plugs ?

If this is a diesel engine you probably have an air lock in the fuel system. It will need "bleeding" before it will start. If you have already tried bleeding the fuel system there may be an air lock in the injectors. If it still doesn't start I suggest you carry out a compression check because diesel engines need to be in good condition to start easily, especially in cold weather If it is a petrol engine, there could be problems with engine timing or ignition problems.

Fuel pump may have ailed this time.. You need to have fuel pump checked.

Have you checked the fuel pressure at the injector ? It has to be at least 60psi for the engine to start.

If it's not working at all, it won't be delivering any fuel to the engine. When you crank the car to get it started, do you smell fuel? If not, try removing the fuel line (most cars this is easy to remove near the fuel filter). Put the unattached end of the fuel line in a container to catch any fuel that comes out. Crank the motor a few times. Any fuel? If so, the pump works (at least partially). If not, it's dead.

This routine varies by car and location of the fuel pump. Auto Zone usually has online repair manuals for free on their site. See if you can find one there.

Your problem may be one of the following:
First check or just replace the fuel filter. Usually located under the car in front of the rear axle, drivers side.
Next, the fuel pump may be worn out. Usually they get loud or stop working (running).
Next, check the fuel pressure regulator. Usually located on the front fuel rail, drivers side.
Is the vacuum line attached? Not leaking or rotted?
Also, do you smell a strong fuel odor when it won't start? May be one or more stuck-open injectors, or the coil pack is bad.
Checking these in the order listed will more than likely fix your problem.
The clicking noise indicates the battery can no longer run the starter, which also means the fuel pump won't run either.
It could be a fuel issue. How old is the fuel filter? Can you hear the pump run for a few seconds when you turn the key on? Try turning the key to ON without trying to start engine three times waiting for the pump to stop running each time. Then try to start the engine. If it starts, Its a form of Vapor lock caused by the extreme heat we have had lately, and a weak fuel pump.

If none of this works, try a new fuel filter first. From there have someone check the fuel pressure regulator and then the pump. If you are in need of a new pump, take my word for it and spend the money to get one from a Dealer, and not from your favorite parts store. Most parts store parts are made in China and they are JUNK.

I had a Grand Prix one time (basically the same car) that had a problem with the fuel pump harness. This harness plugs into the top of the fuel pump as you know, and into the floorboard underneath the car. Check the floorboard end for corrosion or broken wires.

When you changed your fuel pump did you also change the fuel filter? If not, that would be the next logical step. While you have it disconnected you can also check to make sure the fuel pump is pumping the fuel.

seems as if the system isnt priming itself when you first move the key to ON in which the fuel pump would kick on for just a moment to prime the carb with fuel if it doesnt sound like the fuel pump is starting at that moment there might be a problem with the fuel pump or a relay going to it or maybe a fuse relating to the fuel pump