Fuel pump not working

I see the fuel pump is fed from two relays with one relay feeding the other. The circuit opening relay in the driver side j/b behind left kick panel is fed from the efi or f-htr relay in the engine room j/b located left front under hood.
It is fed from the ignition fuse in the instrument panel junction block, located left side of dash.
So, remove that circuit opening relay and test the spots in the empty socket for voltage. The same one that has voltage for the first two seconds when the key is first turned to run will be the same one that has to be hot when cranking the engine over. If it is not, make sure that ignition fuse is hot with the key on start.
If on the other hand the circuit opening relay spot is hot with the key on start, then the problem has to be with grounding that circuit opening relay and that is done by the ecm, most likely from a signal from the crankshaft position sensor telling the computer that the engine is turning over. So if that is the case first try seeing if there are any trouble codes stored in the ECM or just try a new crankshaft position sensor.

It is possible a faulty crankshaft position sensor would also cause a no spark. Does your scan tool read cranking rpm's, if so see if you get a cranking rpm of around 100 rpm or so, if not then you should suspect a faulty crankshaft position sensor.

Normally you will not have the pump on during cranking. The system should turn the pump on for about two seconds as soon as the key is turned on. Then when you crank the engine the pump will not turn on until the ECM receives a signal that the rpm's are increasing from cranking speed.
If you have bypassed that and the pump was running but the car still did not start you will want to check the actual fuel pressure in the system. Spec is 44-50 psi. A bad regulator or worn pump may drop the pressure enough that it will not run.
A way you could test quick would be to shoot some engine starting fluid into the intake. If it tries to run then you have a pump or injector issue.

Not if it is not creating enough pressure or the injectors are not being activated.

Easy way to test that is to pull a connector off an injector and hook a test light up and see if it flashes during cranking.

Did you connect the test light across the connector or connect it to ground and probed each wire? You need to connect it in place of the injector. One side will have power with the key on, the other side will be switched to ground through the computer.

That is what I thought. Easiest way would be to connect the test light to the battery positive post. Then gently probe the connector pin that did not light up when you tested. Now crank the engine. The light should flash if you have injector pulse.

Or go to a parts store that has loaner tools and borrow a set of Noid lights. Select the proper one and plug it in. It will flash if you have injector pulses.

While you are there you could also borrow a fuel pressure gauge and verify that as well.

Does it come on when you first turn the key to on? If not check the relay as indicated above.

OK, So the engine will try to run on starting fluid BUT you don't have the initial pump prime but the pump does come on if you crank the engine, but the pump doesn't keep running. Is that a correct summary?

So the computer is not seeing the engine crank over or you are losing power to the computer system somewhere. I would start by checking the circuit open and EFI relays. Here is a guide and the engine wiring diagram o you can see how the system works.

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

Does the ignition have spark?

https://www.2carpros.com/articles/how-to-test-an-ignition-system

Here are the relay locations (below)

Check out the diagrams (Below)

Please let us know what you find. We are interested to see what it is.

Cheers, Ken

O yes it is very possible.