Power brakes not working. I connected the test vacuum pump to the valve on the booster and it would not hold any vacuum. I tested the valve off of the booster and it worked properly. I tested the booster connected directly to the vacuum pump and it held no vacuum. This would indicate the diaphragm in the booster is bad. Correct?

Yup, sure sounds like it. usually when a diaphragm goes bad somebody ends up pregnant but in this case you should be able to here a slight whooshing noise inside the car where the pushrod enters it when pushing the pedal with engine running. If you are concerned with originality on your car there are letter codes on the booster and if original you can have them rebuilt.