Your Noah b. abt. 1790 d. 8-20-1851 was married to Elizabeth Godwin 2nd. He was married first to Unknown and had children. Noah and Elziabeth's daughter Nancy b. abt. 1837 was married to Hiram Godwin b. abt. 1835. They had 4 known children--Elizabeth, Thomas, Nancy and Mary.
I have never known this Noah to be called Noah G. or having a middle initial.