Many may be having trouble locating their ancestors purely because the surname was changed when the emigrates came to America. Per the following from the Journal of the American-Irish Historical Society, Volume 15 from 1916/1917 page 159.
"Since the original emigration of the O'Donnells the name has been spelled in various ways, Dunnel, Dwinell, Dwinnel, Doniel, Dunwell and Donell; but the origin of each one and of every one is O'Donnell, of Ulster. These O'Donnells came over between 1641 and the outbreak of King Philip's War in 1675, at just what time it is not certain. While one well-known member of the family, Michael Dunnel, as he spelled the name, settled in Topsfield, Mass., many of the others came to Rhode Island, and from then forward were prominent in every branch of the colony's activities. And this is but a single example of the manner in which the original Irish names have been changed, intentionally in some cases, carelessly and thoughtlessly in most, until, to the superficial observer, the real origin of the names and families has frequently been lost sight of, or misunderstood."