Martins sister Elizabeth is in Yalobusha Co., MS from 1880 on, so that might be another place to look.
Martins sons Andrew and James both died in Memphis between 1929 and 1931. Death certificates for Shelby county are on line, but I did not find one for a William Parker where the age matches.
Tell me where you got the information about the marriage and any other documented evidence that he lived past 1870 and I'll try to help you find him. There are several William Parkers living in N. Mississippi from 1870 on, but I can't link them to anyone else at the moment.