I have a '66 SS. Has drums (power) all way around. The brakes work well. When the brake pedal is released, the brakes stay on. Only once the car accelerates quite a bit do they let go.

What should I do to diagnose and fix this problem?

Thanks,
Gerald

I went out and drove it a little to see more closely what is going on. Idling at ~5mph I put on brakes hard.... came to full stop.. let off brakes..... brakes stayed on....after about 15 -20 seconds, I could hear the rear brakes releasing and the car began moving forward.

There was a fellow TCer that recently had a simular problem to what you are describing with his rear brakes.His fix was to replace rear flexible brake line above center of rear end!He found the problem by blowing through it.
I would check to see for sure which corners are draging by jacking up and turning tires by hand after the go and stop test.
Report your findings and someone here will surely help you along...
You may want to do several go and stop tests!

I had the same problem on my front left wheel and it was the hose. The hose was not very old but it was colapsing on the inside. Changed the hose and no more problem