James Sharples: Mar. 2, 1841 - Sept. 11, 1924

I'm researching my family ancestry from Wigan and I've hit a brick wall. James Sharples (b: 1841) was the son of Elizabeth Sharples (1816-1910). Upon his birth, Elizabeth gave James her surname, Sharples. No father is listed in any documentation that I've come across. James was baptized at All Saints in Wigan, living on John Street at that time. 1851 census shows James and Elizabeth at the Wigan Workhouse. By 1861, I suspect that Elizabeth had married John Melling (1818-1890) and James had married Jane (nee Baldwin)(1846-1928).

I'm trying to find out the birth father/surname of James. DNA testing and Ancestry research has been inconclusive thus far. Any help would be immensely appreciated.