Wierd starting issue
 

Yesterday, when I attempted to start my 1977 S the fuel pump ran, dash lit up, then a loud "click" from the engine compartment. At that point, all electrical power was gone. I checked the connections, fuses, etc. Nothing. After about an hour I noticed the light under the front hood was on. I attempted to start it again with the same results as before.. After about an hour, power again. This cycle continued two or three more times.
Any suggestions? It seems like something is closing (the click) and then gradually reopening. Solenoid, voltage regulator etc?

Only guesses here, given what you've posted.

How old is your battery, and how are the connections to it? The "click" may be the starter solenoid engaging, but it's possible the starter is stuck or you have a huge current draw that effectively "kills" a weak battery. Or, the current is causing heating of the connection to the battery and causes it to break the circuit.

Have you checked the charge of the battery? Try an overnight charge and see what happens.

Do you have an alarm system? It sounds like an immobilizer.

I had a very similar problem with my car, turned out to be a loose earth wire on the starter.

Bad battery, bad ground or bad connection to starter. With the key off, turn on your headlights. If they are dim, it's probably your battery.

Yes, It does have a kill switch installed that runs thru the MSD unit. I'm going to remove it first. I thought of grounds also. I'll check and clean the ground wires also. The battery was fully charged, but I'll put the charger on overnight just in case.
I had problems like this before on other cars, but not the instant loss of ALL power. That's why I thought that something was stuck either open or closed. I'll post my results this weekend when I have a chance to work on it.

In looking at the locations of everyone who responded, you all live where it is warm!
Being that I live north of the imaginary line, I am familiar those symptoms and I would point at the battery. It is most likely a dead cell or the battery is getting tired. With a dead cell the lights will look almost right but as soon as you try to start the car CLICK. There is just not enough juice coming out of the battery to supply the required current to start the car. Also, if your alternator overcharges a bit the fluid level could be low in a few cells. In both these conditions the battery will seem to take a charge.
You could also check by using a volt meter. If you think the battery is fully charged measure the voltage with nothing on and the charger not connected. If it is less than 12 volts you have a bad cell, the battery is tired (meaning the plates inside have oxidized that how they wear out) or the fluid is just low. Rarely a cell can go bad due to vibration or impact from dropping.
Let us know how it works out
Barry

Bad battery ground. Try it, if it does the same thing then wiggle the ground at the battery. Happens all the time to me in my bus because I am to lazy to fix it correctly ( I frequently remove the battery to start rc airplanes so it is always hand tight)

Today I installed both a new battery and ground strap. Started and ran perfect. Thanks.