My 1966 Plymouth Fury won't start.

What's the symptom? Doesn't crank or it cranks but won't run? Does the starter relay click? Have you tried it in neutral?

There's a dozen places to test for voltage so you have to be more specific when you say "it has voltage". You can split the system into three distinct circuits, the low-current ignition switch circuit including the coil part of the starter relay, the medium-current part including the starter relay contacts and starter solenoid coil, and the high-current circuit that includes the solenoid contacts, starter motor, and both battery cables.

If you don't hear the starter relay click when you turn the ignition switch to "crank", it's the low-current circuit that has the problem or there's a problem with the battery / cables. Turn on the head lights and see how bright they are. If they're bright, see if they stay bright when you try to crank the engine. If the lights go out or get dim, you have a battery or cable connection problem. If they stay bright, there is a problem with the ignition switch, neutral safety switch, starter relay, or wiring between them.

See if this page helps:

http://randysrepairshop.net/chrysler-1960---1980s-rwd-operation.html

AGGGHHHH! DO NOT DISCONNECT THE BATTERY while the engine is running! That is a real easy way to destroy stuff on the car. The generator can have all kinds of different problems yet the engine will stay running without the battery so that test is meaningless. It was a trick done many years ago by untrained mechanics who didn't understand how these simple systems work.

First of all, what kind of car? Year, model, engine size, etc.

Second, you're doing yourself a disservice by piggybacking on this post. Only I will get an automated e-mail telling me a reply has been posted and it will direct me back here. No one else is going to see your question or have the chance to respond. I'll help you if I can but I'm not an expert on all cars and models.