The birthdate of Cornelius Gillett, Sr. in America listed as January 10, 1634, is suspect as it predates the likely arrival of Cornelius' mother Mary Gillett from England - sometime in mid-1634, following her marriage to his father Jonathan Gillett, Sr. in March 1634. As far as records go - Mary was not in America prior to that point - only the Johnathan Sr.
FYI - This is my first comment on this site, so please forgive me if I am not following protocol. I am related to a younger brother of Cornelius.