Without knowing more about the course grant, I wouldn't be able to fully advise on that part, unless it is DSA but that doesn't have a qualifying benefit restriction. However, the DWP aren't saying you aren't disabled (because obviously you are in receipt of ESA, so there must be some element there), but that you aren't in receipt of the qualifying benefit. There is a difference.
Have you previously applied for DLA/PIP? If not, you would probably be better asking CAB about your eligibility for that. CAB advisers are not placed to be advising on trying to take on a government department for a legal challenge under legislation. They would be able to help you get a mandatory reconsideration and then an appeal if your application for PIP/DLA was rejected though.