For any gasoline engine to start it has to have fuel. Check to see if your getting gas in the carb. You may just need a fuel pump.
Bad ignition switch or starter solenoid
The starter solenoid, or ignition switch is bad, and either one needs to be replaced.
Check the neutral safety switch,it is located on the transmission or on the steering column ,under the dash.
Probably not a bad ignition switch, but more likely a bad starter solenoid. It takes a lot of current to get a starter to turn, to much to go through such a small switch like the ignition switch. The ignition switch actually controls a relay(solenoid) which can handle the needed current to get the starter going. On a lot of modern cars the solenoid is built into the starter unlike older cars and trucks where it was mounted on the firewall between the battery and the starter.
Check your ingnition cylinder ...
This could be a bad ignition switch, ignition relay, or ignition fuse.
Your neutral safety switch-try putting car in neutral and trying it
Starter Ignition Neutral switch
might be starter relay, or the crank circuitry from the switch or to the starter from the relay. I would trace back from the starter to the starter relay back through the neutral safety switch to the ignition switch.
Check fuses and relays. If you have power coming from the ignition switch but not getting to the starter there might be a bad fuse or relay or wire. Also make sure you have the wiring correct to the starter since you just replaced it.
Bad ignition switch or starter solenoid
The starter solenoid, or ignition switch is bad, and either one needs to be replaced.
tighten the nut from the starter to the solenoid
Try an ignition switch.
Check the 92 Camaro neutral safety switch next. If the switch is faulty then the starter will not get power to start the engine.
Could be a faulty ground wire. Not very rare to happen
you need to have the starter solenoid checked. also check thew ignition switch