OK, here's the problem:

Out of nowhere, the trans am just decided not to crank over at all. So today I replace the solenoid, and it starts right up again.
Then 10 minutes later, I go to start it, and it's totally dead again.

So now I have no clue what to do. Does anyone know what I can do to get it reliable again?

Also note that there seems to be an extra wire on the bottom post of my starter. My '80 Camaro only has the +12V and the Ignition wires. This other wire is a very thin black wire.

Can ANYONE give me a solution to this????

 

You replaced just the solenoid?? Go back to the parts store and get the whole starter/solenoid combo and bolt it up.

Also check both positive and negative cables, starting at the battery and inspecting the entire length of each all the way to the other end. Then ensure the terminations at both ends are clean and tight. If in doubt, remove...clean...reinstall securely.

If still no go after doing all this, check the starter interlock switch. On automatic transmissions, it's on the shifter mechanism under the console. On manuals, it's on the clutch pedal. Ensure the switch is closing (check resistance across both poles with a meter, should go to infinity when the switch is closed).

 

I had the same problem... It may or not be this, but when my car did this 2 weeks ago, I found that I blew the Fusible link between the Starter and the Battery....

I hope you get it all fixed up!
Good Luck!

 

How do i tell if the fusible link is bad and if it is, how do i replace it?

 

When my fusible link went, I had power to my interior lights, parking lights and what not, but on my firebird my headlights would not pop up, and when I put my key in the ignition and tried to start it, it would not click, or start.

 

The fusible link will be brittle and will break easily IF it's bad. If it's still good, it will be malleable. There are 3-4 links going to the starter. Anyway I bet your car will be fixed once you replace the entire starter/solenoid assembly, like kevinc said.
Good luck!

 

You can isolate the wiring (well, except the battery cable) by momentarily jumpering from the battery terminal to the small "switch" terminal. The solenoid should pull in and the starter should crank over. (Obviously make sure the car can't jump forward and run you over! )

You say a wire is connected to the OTHER terminal? That's there for the old-school pre-HEI distributors that used a ballast resistor. This terminal put the full 12V on the coil (bypassing the resistor) to give it a little more grunt when cranking. On an HEI-equipped car (like I assume yours is) this terminal has no function.

And if there's any doubt at all about the quality of the battery cable, you might as well replace it when you do the starter. They're pretty cheap