Tom, at our library we have a subscription to AmericanAncestors.org, the website of the New England Historic Genealogical Society in Boston. They have a lot of early New England records and research and I would suggest taking a detailed look at this when you have time.
I did a quick search on their Vital Records Database but didn't find a Charles or Asa DENNETT born in 1801 in their records. I looked at marriages for that surname between 1817 and 1835. I didn't find a DENNETT with either first name regardless of state of residence but did find the following: Jonathan, Mark, Hiram, William, George, Nathaniel, Moses, Eugene and Joseph. There was a Charles DENNETT mentioned in their journals. He was listed as the guardian of Nathaniel Savory in the New England Historical and Genealogical Register, Volume 39, Page 189, published 1885. - Ed