I've checked out the neutral safety switch - it receives and sends voltage when the key is turned to ignition. However, the small cable that goes to the starter does not give any voltage. I've looked at the wiring schematics, and the only thing that I can see connected in that circuit between the neutral safety and the starter is the ECU. Would an ECU burnout cause this? What else can cause this? I've checked and cleaned the battery ground.
Check your relays. The Schematic shows an "Inhibitor Relay" This should not be an expensive part to just replace. But there are ways to test it. complete a circuit of 12 volts to the low terminals and the switch should change at the high terminals. Check the manual to see how that switch should operate.
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I had a mechanic come out to take a look at the car, and he tried short-starting the starter. It wouldn't go. He told me the starter itself was bad. I had just purchased it, so I removed it and tested it at an auto parts store - it turned out the starter was fine.
This whole time I was also not getting voltage at the small wire which goes from the ignition switch and neutral safety switch to the starter. I checked the voltage on the neutral safety switch while cranking, which showed 12 volts. All of this led me to believe that the ignition switch was bad.
I removed the rear of the ignition switch, but realized that before assuming that it is bad I should first run a jumper wire from the battery directly to the starter to test the starter in the car. I did so, and discovered that the starter did, indeed, work in the car. Then, just for kicks, I put the ignition switch electric housing back in, cranked the key, and the starter worked. Maybe the ignition switch needed to be wiggled, maybe it's going bad, maybe the neutral safety switch needed to be reattached properly. Who knows?
In any case, the new starter works but I still have a no-start condition. My fuel pump relay is bad. Upon running a jumper wire across the relay terminals, I receive voltage at the fuel pump leads, but the pump does not appear to be working at all. The pump and fuel filter are brand new. I will start a new thread to address that issue.