You have two separate problems:
A No crank problem:
No Crank checklist for 5.0 Mustangs
Since some of the tests will bypass the safety interlocks, make sure that the car is in neutral and the parking brake is set. Becoming a pancake isn’t part of the repair process…
Check battery, terminal connections, ground, starter relay switch (also known as solenoid) and starter in that order. The clamp on with 2 bolts battery terminal ends are a know problem causer.
A voltmeter is handy if you are familiar with how to use it to find bad connections. Measure the voltage drop across a connection while trying to start the car: more than .5 volts across a connection indicates a problem.
See http://www.fluke.com/application_notes/automotive/circuit.asp?AGID=1&SID=103 for help for help troubleshooting voltage drops across grounds.
1.) Will the car start if it is jumped? Then clean battery terminals and check battery.
2.) Check the battery to engine block ground, and the ground behind the engine to the firewall.
3.) Jump the big terminals on the starter relay next to the battery with a screwdriver - watch out for the sparks! If the engine cranks, the starter and power wiring is good. The starter relay is also known as a starter solenoid.
4.) Then pull the small push on connector (small red/blue wire) off the starter solenoid (Looks like it is stuck on a screw). Then jump between the screw and the terminal that is connected to the battery. If it starts, the relay is good and your problem is in the rest of the circuit.
5.) Remember to check the ignition switch, neutral safety switch on auto trans and the clutch safety switch on manual trans cars. If they are good, then you have wiring problems.
Typical start circuit...
Diagram courtesy of Tmoss & Stang&2birds
See
http://www.autozone.com/images/cds/gif/large/0900823d80195963.gif for 88-90 year cars
See
http://www.autozone.com/images/cds/gif/large/0900823d80195964.gif for 91-93 year cars.
See
http://www.autozone.com/servlet/UiB..._us/0900823d/80/1d/db/3c/0900823d801ddb3c.jsp for 94-95 model cars.
6.) The starter may be hung, loosen up the bolts that hold it on, and give it a good whack with a big hammer. Tighten up the bolts and try again.
7.) Pull the starter and take it to Autozone or Pep Boys and have them test it. Starter fails test, then replace it. If you got this far, the starter is probably bad.
A fuel pump relay problem:
Fuel pump runs continuously: The tan/green wire has shorted to ground or the relay contacts are sticking.
Disconnect the computer and use an ohmmeter to check out the resistance between the tan/green
wire and ground. You should see more than 10 K Ohms (10,000 ohms) or an infinite open
circuit. Be sure that the test connector isn’t jumpered to ground. If the resistance check is good,
replace the relay.
Diagram courtesy of Tmoss & Stang&2birds
See the following website for some help from Tmoss (diagram designer) & Stang&2Birds (website host) for help on 88-95 wiring
http://www.veryuseful.com/mustang/tech/engine/
Ignition switch wiring
http://www.veryuseful.com/mustang/tech/engine/images/IgnitionSwitchWiring.gif
Fuel pump, alternator, ignition & A/C wiring
http://www.veryuseful.com/mustang/tech/engine/images/fuel-alt-links-ign-ac.gif
Computer, actuator & sensor wiring
http://www.veryuseful.com/mustang/tech/engine/images/88-91_5.0_EEC_Wiring_Diagram.gif
Fuse panel layout
http://www.veryuseful.com/mustang/tech/engine/images/MustangFuseBox.gif
Vacuum routing
http://www.veryuseful.com/mustang/tech/engine/images/mustangFoxFordVacuumDiagram.jpg