The parents for James Ball are shown in the well-researched book "The Balls of Fairfax and Stafford in Virginia" by Bonnie S. Ball, James Elihu Ball and Estella Ball Brady, 1961.
The family of Enoch Ball, b. 1834 in KY, and Charlotte Hampton(?), b. 1840 in MO, are covered in the supplement section of the 3rd edition of that book on pages 30 and 31.
Despite the many trees on RootsWeb, the book states:
Enoch Ball was born about 1834 in Kentucky. He was not a son of Bennett Ball, but he was closely related....
Best I can do.
Compiler of the New England Ball Project