Classic/Antique Car Repair: Ignition, neutral safety switch, mustang coupe

Question
I have a 1966 Mustang Coupe. It's been running fine until recently when I went to start it. It has power (lights, radio, etc.) but when I turn the key all I hear is a clicking noise. I've switched out the solenoid and replaced the wire between it and the starter but still just the clicking noise. Could this be the neutral safety switch or is it something else?

Answer
Usually when the solenoid just clicks it is the sign of a low battery. Time to get the voltmeter out and check the voltage of the battery. A dirty or poor connection at the battery cables can also cause this. Now, have you check to see if the engine will turn over? use a wrench on the front pulley nut and make sure that the engine is not seized. let me know if these are not the cause and we will continue from here.
Brad