OK, what I'm going to write here may not make you a happy camper but here it is.
On reviewing the site for St Augustine, I don't see anywhere that it says their program will qualify one for a state registry as a nursing assistant.
I don't see where they say this is a CNA (certified nursing assistant) program - they say they will issue a Nursing Assistant Certificate (which you write that they did) and not that they will qualify you for any state certification.
While they do write that they are accredited, I can't find by what agency. Accreditation doesn't imply that you'll qualify for certification though. Depending upon which agency issues the accreditation, it may not imply anything at all.
It's very possible that he learned more than $676 worth of information in this program. It seems to me that this school has done exactly what they said they'd do. It's possible that you and your son have read more into what they promised than what they really did.
A nurses aid/assistant (we used to call them orderly) doesn't require any certifications generally. That is a different thing than a CNA (certified nursing assistant). Remaining open minded when you consider this question - did he just finish a program to train "nursing assistants" or "certified nursing assistants"?
St. Augustine has an address on their web page as being in Atlanta Ga. You can contact the Ga. state board of education to register your complaint and they will investigate.
bottom line is, they showed you a chicken, you thought it was a duck and bought it, now you want a duck. But they never offered you a duck to start with, they said chicken all the time.