If you have a living male relative with the Parks surname then I highly recommend going to
http://www.familytreedna.com/cj.aspx?ftdna_ref=600
and pay for him to take the Y-DNA37 test. It will tell you which Parks he does and does not share ancestry with. It may reveal direct paternal line cousins who adopted different surnames. It will likely reveal the origin of this direct paternal line prior to slavery.
If the Parks tester is found to belong to Y haplogroup Q-M242 (or one of its subclades [sub groups]) then the origin of that paternal line is Native American.
Sincerely,