First check the records at Connecticut Index, http://dunhamwilcox.net/0_index.htm
You won't find an official birth record for him since CT wasn't recording births that early. You might find a church baptism in the Barbour Records at CT Index.
Look for their marriage license/record. Both sets of parents names might be on it. The New London Town Clerk should have their marriage record. I'd also contact the New London County Historical Society, http://nlhistory.org/resources/
I'd check the newspaper marriage announcement. Both sets of parents might be mentioned.
The Connecticut State Library has death records 1897-1965. His parents names should be on his death certificate if the Informant knew that information. Successful Searching!