Johnathan Fairbanks Parents?

I am related to the Fairbanks line through Mary Captive (Moore) Kathan. Her husband was Benjamin Moore. Mary's mother was Martha (Moore) Kathan. Martha's parents were John Moore and Hasadiah Fairbanks.
I have a few questions concerning the Fairbanks line and starting to get a little confused. First, who were the parents of Johnathan Fairbanks b abt 1596, England, d. 12/5/1668 Dedham, Norfolk, Ma? (Married to Grace Lee Smith). Also who were the parents of Fairbanks Moore, b ? d. 3/6/1758 in Brattleboro VT? With the first name of Fairbanks, perhaps his mother was a Fairbanks. I would really like to get this family straighten out. Any help is greatly appreciated.
Debra