Captain John D. Hancock was born around 1733 or 1735 in Palmyra, Fluvanna County, Virginia or Albemarle County, Virginia. 
Church of England
John D. Hancock (or Hancocke) married Elizabeth Maddox on October 16, 1755 in St. James Northam, Goochland County, VA. She was born January 1 or 3, 1732/33 in Fluvanna, Virginia and died 1805 in Amherst County, VA or in Goochland County, Virginia or Patrick County Virginia. ELIZABETH MADDOX was the daughter of JOHN MADDOX and ELIZABETH SHERWOOD.  Reverend William Douglas (of "Douglas Register of Goochland") officiated. This is their listing in the Douglas Register:
"Hancocke, John & Eliz. Maddox, both in this parish, 1755, Oct 16," p2
1762 Land transaction
MARCH 18, 1762, John Handcock enters the vacant land between the lines of Benjna Dickson, Jas. Roberts, Wm. Wright and Geo. Currie and Brs. Sandy Creek not exceeding 400 Acs. (1762, 18th March). 
1774, Jun 5 - "In consideration of the sum of 10 shillings of good and lawful money, John Hancock was granted one certain parcel of land, containing 87 acres, lying in Co. of Albemarle, on the S. branches of Cunningham's Creek, beg. at Wm. Moore's corner to pointers in Colonel Hopkins' line, So. on George Hilton's line, East to Thomas Jefferson's line, then on to Wm. Moore's (Morris') line North to beg." [Vol 42, p. 709.]
Children of John Hancock were:
Benjamin Hancock was born 1756 and died 25 Oct 1817.
Lewis "John" Hancock was born 1757 and died 5 Oct 1828.
William L Hancock was born 1759 and died Nov 1849.
Nancy Hancock was born 17 Jan 1763 and died 17 Jun 1848
Rhoda or Rhodice Hancock was born about 1766 in Virginia and died about 1850.
Major Hancock was born 18 Jul 1770 and died after 1849.
Susannah Hancock was born about 1772 in Fluvanna, Va and was christened 11 Nov 1770 in St James Northam, Goochland, Va.
AUGUST 1, 1777, [John Handcock] deeded land to his son Benjamin Hancock on Cunningham Creek and to Lewis Hancock 87 acres adjoining, among others, Thomas Jeffeson.
(1776-1781) Military Service
May have served as a Private in the Revolutionary War or in the Virginia Militia as a LT. under Captain Thomas Blackburn (Revolutionary War)
John Hancock died between November 10, 1802 and December 1802 at 69 years of age in son Benjamin's home in Patrick Springs, Patrick County, Virginia. Buried on the northeast slope of Bull Mountain, 
perhaps at the Liberty Primitive Baptist Church Cemetery.
NOVEMBER 10, 1802
Patrick County, Virginia, John Hancock's will in Patrick County, Virginia mentions his son, Major Hancock. November 10, 1802, Patrick County, Virginia.
"In the name of God Amen. I, John Hancock, of the county of Patrick, being in good health and in my perfect sense... I do make, constitute and appoint this my last will and testament;... my body I give to the earth to be decently buried according to the will of my executor hereinafter mentioned, and as for all the rest of my temporal estate, I give and bequeath as followeth:
Item. I give and bequeath to my son, Lewis Hancock the land whereon I lived in the county of Fluvanna, to him and his heirs forever.
Item. I so lend to my well beloved wife, my sole estate in doors and out doors during her natural life, and after her decease, to my son, William Hancock should have a part of the land whereon I now live; that is from the end of the mill dam on the ridge to the north line to him and his heirs forever.
Item. The remainder part from there down, I give and bequeath to my son Major Hancock to him and his heirs forever.
Item. I give and bequeath to my son Benjamin Hancock all my wearing clothes. [He had previously given Benjamin a farm of 182 acres on Cunningham Creek in Fluvanna Co., VA]
Item. And after the decease of my wife, my will and desire it that the rest of my estate be equally divided between my five daughters and my son William Hancock, to-wit: Nancy Corn, Rodie Lane, Elizabeth Mayo, Judath Mayo, and Susannah Hancock.
Item. And proportionable part with them to be given to my daughter Mary Morrison's two eldest children, to-wit: Allen Morrison and Jency Morrison, to be sold and equally divided among them.
Item. And I do appoint my son William Hancock my whole and sole executor of this my last will and testament.
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with John: