The engine cranks and tries to start when the battery is connected. It does this autoatically, you dont even need the key or ignition to be turned on. The remote silanoid has been replaced so has the starter. The car does start and run when you let it but the starter remains engaged so its LOUD. I have bypassed the ignition switch by disconnecting it entirely, however the car still cranks and wants to turn on when the battery is connected.
Make sure starter relay has a good ground. You should have a heavy ground cable going to engine and a lighter ground cable going to fender or radiator support. And the starter relay needs to be properly mounted to fender so it’s grounded.
Pull the small wires off the solenoid and connect the battery and if the starter does not engage check the wire that was on the S pin of the solenoid. If it is hot follow it until you find the problem.
With age of this car it is possible someone has messed up the wiring somewhere. It seems the solenoid is not getting the message to kill current to the starter. Once the current to the starter is cut off the starter stops and the bendix drive disengages from the flywheel.
It is a bad ignition switch, a bad solenoid, or a wire either crossed or connected improperly. It should not be hard for a good electronic man to figure this out.
I had a '67 Mustang (it was a new car back then) and these cars are not complicated as far as wiring and electronics are concerned. A transistor radio was a big innovation back then.
45 year old automotive wiring simply does not last forever…Sounds like a major re-wire job will be needed to restore reliability to this car…
Starting point. Remove the fuse block from it’s mounting, turn it over and take a look at what the back-side looks like…
Its your starter solenoid…which I believe is mounted on the left or right side of the engine compartment…it is either stuck in the "start position internally or someone put a 12V hot wire on the wrong terminal Rod Knox got it right… A very easy fix actually just find out why the solenoid is in the start position…its either stuck or being supplied with 12V to the trip terminal when it is supposed to be switched 12V to the terminal. GO online and look up the wiring diagram for the solenoid…very easy stuff
Since you have replaced the solenoid and starter already and still have the same problem this pretty much means the small solenoid wire has power getting to it somehow. Normally the power is connected to it through the ignition switch. Like others have already said, remove the small wire to the solenoid and check for power on it using a test light probe. This will give you something to check for power with. Somehow that wire has tied to power before the ignition switch. Pehaps it is tied to the input side of the switch which is always hot. Don’t allow the engine to start while this trouble is occuring, damage will occur.
Possibly the S and I wires are crossed at the solenoid.