I have a 68 Dart in storage and I periodically start and run the car. Had the car running briefly but had to shut it down to take a phone call. Came back out next day and went to start it and heard a "clunk" when I turned the key to start - lights and all electrical go dark. I disconnect the battery and reconnect - lights are back on - go to turn the key I get the noise and no electrical. To triple check did it all over again and same result. I swapped our relay and issue remains. Any ideas would be appreciated. Thanks!

Check both ends of the battery cables and charge state of the battery.

First thing to check is the battery. An approximate check can be made with a voltmeter. Assuming 'room temperature' 12.8 Volts would be good. Below 12, don't bother with more tests - recharge it. Further test would be to turn on the lights, it should not drop much. Lights off, cranking, it should stay above 11 V if full charged.

If there is some problem in a circuit:
The Headlights are wired direct from the main splice. No key needed.
The ammeter is wired between the battery and the main spice. It too will work without the key on.
The other instruments will get power when the key is on.

To add to the above, could be a voltage drop issue. Dont forget to check the ground side of the circuit. You may have a connection, but with corrosion, not enough to handle amperage.

Agreed, clean every large cable end/terminals including ground cables/straps