My 64’ falcon wont start. The starter is about 4 months old, same as the battery. The starter makes a loud click, but it will not turn the motor. It doesn’t sound like the click a bad starter switch makes. It sounds like the starter cannot turn the motor. The car has plenty of oil.
also, the car was running very rough when I parked it.
To determine that, just place the shifter in neutral and try turning the engine over by hand with a socket/ratchet on the crank pulley bolt or use a pipe wrench turned sideways on the crank pulley.
If you can’t move it by those methods then you need an engine or engine rebuild.
I would add that you should pull all of the spark plugs when you try turning it over. It’s possible the carb bled over and got fuel into a cylinder and caused a hydralic lock in one of the cylinders.
My suggestions is to pull out the spark plugs, squirt some penetrating oil into the cylinders through the spark plug holes, and without replacing the spark plugs, try to turn the engine over either with the starter or a breaker bar attached to the crankshaft pulley. Let the oil set in the cyliners for a half an hour or so before you try to turn the engine. If the engine turns over, squirt some motor oil into the cyliners and turn it over a few more times. If and when you get the engine running, drive it gently for a couple hundred miles and then change the oil.