It almost sounds like something between the ignition switch and the soleniod switch. Put a voltmeter on the battery, and while trying to crank - see if there's a load. If so, then your starter is most likely the culprit. If no load, then check the soleniod to see if the ignition switch is switching 12V to it. If not, then troubleshoot relays that are in series with the output of the ignition switch to the input of the solenoid switch.
I fix an Integra last week that had the same symptom. There was no switched
12V to the SS (solenoid switch). I could jumper the 12V to that terminal on the SS and activate the starter. I found a relay that had to be tapped on a few times...to jar the mechanical switch in the relay....and it's still fine.
Good luck.
I recently got a 1990 Pontiac T/A GTA. It has the 305 w/ 5 speed
> manual. IT ran fine until last week when I put it up on some
> jackstands to change the oil and plugs. It now will not even crank at
> all. When I get in the car, and turn the key I can hear the fuel pump
> turn on, and all the lights come on as normal. The security light
> comes on for 5 sec and goes off. The check engine light stays lit.
> When you turn the key nothing happens. No clicking, or anything. When
> the key is turned the Brake light comes on and the coolant temp goes
> to the highest spot, (they go off once key is released). I have
> checked and double checked for disconnected wires but nothing seems
> bad. I pulled the codes and the first time I got a 46, but I cleared
> the codes (as it could have been old) and now I just get the 12 code.
> The only thing I did on the car is to clean the TB. Could damage to
> one of the sensors in the TB cause this condition?? Please help.