Thank you for posting your request on History Hub!
In regards to finding the father of David Warren Fuller, I might suggest conducting a search of vita records for the states where you believe he might have been born. Based on his date of birth, and the two states you believe he might have been born in, I would suggest reaching out to the following two agencies:
The Massachusetts State Archives:
And the Vermont State Archives:
Vital records, ie, birth, death, marriage, divorce record are state level records and are not held at NARA.
I hope this is helpful in your research!