The fuel pump of my Saturn is not getting a signal. It will run if I jumper the relay and I will get fuel to the fuel bar. The relay tested good and I also tried swapping relays. Any ideas of what to try.

The fuel pump only gets power when the engine is cranking over or it is running of course. Jumper the relay to test the line.

If you jumper the fuel pump relay under the hood will it start.

Test the relay base, if it has everything it is suppose to and the circuit still does not operate then the relay is the reasonable suspect. The base should have a constant 12v power supply, this can be tested easy enough with a test light or multimeter set to DCV. one of the other pins should get a 12v signal when the key is switched to the "on" position. another of the pins should have continuity to ground, and the last pin should go to the pump itself. If you put a jumper wire from the pin with constant 12v signal to the one that goes to the pump the pump should run. If the pump runs and you have all of the correct signals at the relay base, then the relay would be the culprit. If the pump does not run when the pins are jumped out then the pump would be the problem.

First make sure all grounds are good. There is a ground going from the pcm to the engine. Many chevy engines had a pcm ground connected to the thermostat bolt. Not sure about the Saturn. A common problem is that someone replaces the thermostat, and forgets to reattach the ground, or to tighten the ground securely. If the car was worked on recently, I would suspect a loose ground.

How is it "tripping" ?
The pump gets a signal from the ECM as long as the ECM knows the engine is running.
Is the check engine light on ?

I'd have to test when problem is ongoing. When you first turn on key, no crank, you should hear the pump run for a few seconds then stop. For initial prime, the computer doesn't need rpm signal. Engine cranking, the computer needs to see rpm signal or it won't ground the fuel pump relay. W/o rpm signal, no spark at the plugs and no fuel injector pulse. I know your talking about fuel, but, when problem is ongoing, check spark and fuel injector pulse, engine cranking.
Intermittent problems are a pain, have to test when problem is ongoing.

If the fuel pump does not prime either the PCM is not sending a ground signal to the relay, the relay is bad, or there is an issue with its circuit (no power to relay/blown fuse, short in wires).
Your injectors not spraying may be the ignition module. The module sends a signal to the PCM to let the PCM know the engine is turning and running. If the PCM does not see this signal it may think the engine is not running and when it does not run it does not spray fuel.
Take the module to an autozone to have it tested.

probably the crank sensor, above the starter on the firewall side-no crank signal, no fuel pump activation.

Hi, if the car runs with the jumper wire, maybe the wire from the ECU is bad. The pump is powered by the 30 amp fuse #1 in the box under the hood. The relay coil is powered by the EEC power relay, and receives it's ground connection from the ECU. If fuse 1 is good, odds are the relay is not getting the ground signal. You can verify this by connecting a test light to the positive battery terminal and probing the relay socket. The pump terminal will dimly light the test light, and when the key is on the ground signal from the ECU should make the light bright. If you don't get this light, either the ECU is not turning the pump on, or the wire from the ECU is bad. Going back to my first question--does the car run with the jumper? If yes, I would guess the wire is bad. If no, I would say there is a reason the ECU is not trying to turn on the pump--like maybe a security system or safety interlock. An easy way to force the relay to come on is to cut the tan/light green wire from the ECU and ground the side that goes to the relay. The pump will run when the key is on, but the ECU will noit be able to shut it off. Please let me know if you have questions.

Maybe you need to test the (pcm) power relay, it controls the fuel pump relay. Once the key is turned on the pcm will initialize the power relay, it in turn will turn on the fuel relay for 2 seconds to prime the fuel rail prior to starting. Since the pump runs continuosly, it means the pcm isnt properly grounding the ckt or the relay is faulty.