Here is what I would do.
As you already checked the battery. I myself have a very nice fully charged optima yellow thing that couldn't even crank the engine ones. Swapping battery's or even better hook an extra on with jumpercables. If you're sure that isn't the problem then move to the next.
Several posibilities.
- ignition switch bad?
- neutral safety switch bad or with manual clutch switch bad?
- any orginal or after market alarm in the way?
- maybe something else?
You can check if it's any of these 3 by short circuiting the starter from the big power cable to the small 12v connection on the solenoid. By very carful when doing this and make sure the car is in Park! If the starter works then the problem is somewhere in the signal wire from the fusebox to the starter solenoid.
Best way to tackle this:
Take a look at your wiring diagram in your service manual. If I'm correct power for the ignition switch comes from the 2 fusebly links that connect to the starter, are they attached the right way?
Your ignition switch (on top of the steering column) has a seperate pin for the 12v that goes to the starter solenoid (in the wiring diagram it's called sol at the ignition switch). You can check the switch if it gives 12v to the starter when in the start position. On my 81 it's the yellow wire (don't ask me how I know :ugh).
If this is oke move to the next or begin with this in what order you like...
The neutral safety switch on a automatic located next to the gearlever under the console, if this is broken or had a bad contact 12v wouldn't reach the starter solenoid. To quickly check you can bypass the switch with a cable by "shorting" the 2 poles from the switch connector. On my 81 yellow and purple wires. Manual transmissions have the same principle switch but at the clutch under the dash, same test can be done.
From the safety switch a wire (purple on mine) goes to the original alarm relais you can check for 12v on the incomming wire. You can also bypass this relais but make sure you have the right outgoing wire. If you have an aftermarket alarm make sure the fuse is still good and if it's on in the off position when you want tot start the engine. As far as I know from the original alarm relais one or two wires go directly to the starter solenoid.
Maybe something else? You can folow the wiring diagram wiring from the ignition switch to the starter solenoid, maybe your 80 has some other features mine doesn't that you can locate in the wiring diagrams.
I would begin with the easy part and that is the neutral safety switch.
And btw, normally it's not something very difficult so I hope you don't need any info from this reply.
Greetings Peter