I have a 1970 with power brakes.  For several months, I have noticed that it takes a few seconds for the "power" brakes to start to work.  Over time, it has taken longer and longer, and now, they never work.  The brakes feel like manual brakes.  It stops fine, the pedal is plenty firm, just no power assist.  I have removed the fitting from the power brake booster and it feels like I am getting plenty of vacuum to the booster.  Also, I have no problems with the headlight doors or the windshield wiper door.  Also, the vacuum tank seems to have vacuum.

Sounds like the booster has problems. The other systems like the headlight openers run on vacuum as well, but I think there is one-way valving and relays in the line to keep one bad system from affecting the others.

Unhook the vacuum line from the booster and plug it, then drive the car and see if it drives any different. That will help eliminate any other sources of vacuum problems.

I imagine you can hook up a vacuum tester to the booster and see if it holds vacuum. If it doesn't, there's your culprit. It could be as simple as the fitting on the booster where the vacuum line hooks up, or it can be internal.

Hope you find it quickly.

Definitely sounds like a booster issue. Do you hear any "hissing" sound inside when you first push on the brake pedal now, or when you first noticed the problem?

If you push on the brake pedal, and start the car, the pedal should go down an inch or so. If not, the booster is bad, or there is a vacuum issue.
To test the booster with a vacuum tester, such as the "Mity-Vac" or similar is a real pain. On the other hand, it will build up the muscles in your hand!
Try the push and start test above...that will tell you if the booster has failed, if you're sure there is sufficient vacuum going to it.

I had a similar issue on my 72. Pedal was extremely hard, brakes seemed to work OK until I had to really put the brakes to the test.