The fuel pump and starter among other engine control items are controlled by the ECM which in turn is also controlled by the BCM...Body Control Module...via power or signals from the ignition switch. Do the injectors click or fire when cranking? Do you get spark? those may show an ECM or powertrain control relay issue if not.
I would perhaps start by testing for power at the starter relay...coil side... which may show if the ECM or BCM has a problem. And test for power out at the ignition switch...white/black wire to BCM..for the starter circuit. GM has had a lot of issues with them so that might be the main problem or an issue for starting. The starting circuit also relies on a Neutral Safety switch or Clutch switch ground path to enable starting so long as the shifter is in Park/Neutral or clutch pedal is depressed.If that path is not working...bad wiring or switch..., then the ECM will not power the starter relay.
If you have some testing skills and tools, then test for power at the starter relay socket that corresponds to terminal 86 of the relay...purple/white tracer wire. That wire/terminal gets power signal from the ECM via BCM when the key is turned to Start position which closes the coil side of the relay via a ground wire...that in turn closes the contact side of the relay which gets power from a 20 amp fuse and then sends power to operate the starter solenoid.
Have a helper turn ignition switch to Start and test for power at terminal 86...if you get no power, then the ECM is not sending a signal...which could also be a BCM issue or ignition switch issue...or Neutral Safety switch issue. If you do get power at 86, then check for a loose or bad ground wire from the relay...terminal 85. If you get power and ground, then test for power at terminal 30...if not then check for blown fuse, bad wiring, etc..
There is also a Powertrain Relay in the fuse box under the hood which controls many engine control features such as coils, injectors, fuel pump, etc... and is controlled by the ECM. Possibly that relay is bad as well ...or not getting a signal from the ECM....which would prevent the pump and starter among other things from working. Check if you have power at coils or injectors with key on ...if not ,then the powertrain relay is suspect. See page 5-101 in owners manual for that relay location....labelled PWR/TRN RELAY
http://www.vadengmpp.com/owners-manual/saturn/2008-Saturn-Vue.pdf
The Fuel Pump Flow Control Module is located in the trunk area if you need to test that...info below. No pump relay in the circuit.
http://arrc.ebscohost.com/searches?car_uuid=1440281&fa_uuid=d8c95920-aec6-012a-3b82-f9a2316539f8&filters%5Bservice_information_type_path_facet%5D=root%2Fmrt%2Fsit%2Frepair&keywords=fuel+pump+module+
Wiring diagrams ...listed under Engine Controls ...or Starting circuit.
http://arrc.ebscohost.com/searches?car_uuid=1440281&filters%5Bservice_information_type_path_facet%5D=root%2Fmrt%2Fsit%2Fp5_diagrams&filters%5Bsystems_component_path_facet%5D=root%2Fmrt%2Fssc%2Fp5_engine_controls%2Fengine_controls_circuit%2Fengine_controls_engine_controls_circuit_1_of_5