Sudden loss of power

I posted something yesterday about possibly taking my '67 Dart 270 (225cid L6 automatic trans) on a 12-hour drive. It's not going to be doing that any time soon because ...

I was running errands yesterday and everything went well. In fact, the car has been remarkably stable over the past two months -- such that I thought I'd worked out all the major kinks in the system. At my last stop, I parked the car and turned it off. When I went to start it again, I turned the key and nothing happened. I opened the door and realized that the dome light wouldn't come on. None of the electrical stuff was working, period. Tried to jump it, but no dice.

As the inner debate raged about whether I should just push it into a ditch and forget it, I got out my handy multimeter to do some checkin'. The connections seem good -- battery (12.7V), battery-to-starter relay, battery-to-starter solenoid, starter relay-to-starter solenoid, battery-to-alternator, battery-to-engine block. It all checks out. The brown wire from the starter relay to the starter solenoid reads 0V, but I'm not sure what to make of that.

I thought it might be something with the transmission (maybe the car didn't "know" it was in park), but that wouldn't cause a loss of power, would it? Also, when it came time to push it onto a trailer, it switched into Neutral fine and back into Park without a problem.

This one has me stumped. Any direction or advice is appreciated.