1988 Mustang won't start

Check the contactor or starter solenoid, it is high amperage switch from battery to Starter, and there are cheap china replacements out there that have a poor ground contact internally, not bonded just loose inside, I had a new one put in and it failed about 300 miles later intermittently, so I put in another AutoZone (cheap) one. You can ohm out the terminals with a meter, and/or check voltages while starting on it. Next to battery and coil driverside bolted to body

more stuff..... what kind of sound did it make when you tried to start it ? clicking? starter OK You could have bad battery, or alternator, or wiring from alternator to battery(is resistance wire)

Yes, it just makes a clicking sound. So far, I have changed the battery, the starter, and the solenoid. I checked all the connections.

What really has me confused is why can't I push start the car. I can hear the fuel pump cycle, I have 12v at the hot side of the coil.

What I normally do with this type problem is jump the starter solenoid with a heavy piece of wire. If the starter turns over you've eliminated the starter and the battery as the source of your problem. If you place the ignition switch in run, when you do this, the car should start. If you've never done this, all you have to do is just take the wire, or you can use a jumper cable, and just bump touch the big terminals on each side of the starter solenoid at the same time. It will spark but if your battery and starter are good it should turn over.

For what its worth

I had checked all the normal stuff. The battery was fine, bench tested the stater, it was fine, changed the solenoid, still nothing. I ran another ground strap from the engine to the battery and that took care of it. I seems that I lost the ground from the engine to the body.