I've looked around on WikiTree and can't find his profile - not sure what documentation you've already retrieved without checking your sources. Would be much easier with a profile to reference.
That aside, here is what I can find:
"Find A Grave Index," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVK2-3TB7 : 13 December 2015), John S. Barnett, 1894; Burial, New Albany, Floyd, Indiana, United States of America, Mount Tabor Cemetery; citing record ID 48385964, Find a Grave, http://www.findagrave.com.
"United States Census, 1870," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MXXV-K95 : 17 October 2014), John Barnett, Indiana, United States; citing p. 7, family 50, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 545,812.
"Indiana Marriages, 1811-2007," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:XFMQ-HFM : 21 January 2016), John Barnett and Eliza Garretson, 13 Mar 1859; citing Floyd, Indiana, United States, various county clerk offices, Indiana; FHL microfilm 1,411,884.
"Indiana Marriages, 1811-2007," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:XFMW-P4V : 21 January 2016), John Barnett and Mary A Young, 24 Apr 1876; citing Floyd, Indiana, United States, various county clerk offices, Indiana; FHL microfilm 1,411,885.
"Indiana Marriages, 1780-1992," database, FamilySearch(https://familysearch.org/ark:/61903/1:1:XF6R-8MD : 3 December 2014), John Barnett and Mary A. Young, 24 Apr 1876; citing reference P407; FHL microfilm 549,333.
The following Census record from 1830 for John Barnett of Floyd County is BLANK - not much help
"United States Census, 1830," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:XHPC-RPR : 18 August 2015), John Barnett, New Albany, Floyd, Indiana, United States; citing 360, NARA microfilm publication M19, (Washington D.C.: National Archives and Records Administration, n.d.), roll 28; FHL microfilm 7,717.
I see no clear parents, so I guess I struck out. Sorry.