Fully Charged Battery - No Power

The starter is not going to make the engine stall or the head lights not work.

How did you determine the battery was fully charged? Do you have a digital voltmeter and know how to use it?

GM likes to use fuse link wires that tap off at the large starter terminal. I'd look there first. If you tug on them and they act like a wire, they're okay. If they act like a rubber band, they're burned open. I can't think of anything that would cause such a severe short while the engine is running to burn one open. I think it's more likely you're going to find one of them just got tired of being a fuse link and corroded apart.

You can also measure the voltage on the large output terminal on the back of the generator. If battery voltage is missing there, again, suspect those fuse links.

Also look at the fuse box and wiggle the harness going into it. In the late '70s GM started using aluminum wires in some cars. When you have two different kinds of metal and an acid, such as road salt, you get "galvanic action". In other words, you have a battery and corrosion. There's brass strips and rivets in the fuse box that the aluminum wires were riveted to, and the box sat right above the driver's feet, right where road salt and water could migrate to it. I found that on a Firebird once that had intermittent tail lights. The only aluminum wires I saw were for the rear harness. To fix it, I soldered some new copper wires to the brass strips in the fuse box and ran those to the back of the car. The insulation on those wires is translucent and you can see the wire inside. Don't poke the insulation to take a voltage reading, (never an acceptable method on any wire), because moisture will get in and corrode the wire apart at that spot in a few months.