Immediately, after finding the death record and obituary of Daniel Moran, I searched for the obituaries of his sisters, Catherine Moriarty and Mary Haley, both of whom had lived in Ware. (Catherine had been misidentified in Patrick's obituary, but was correctly named in the obituary for Daniel, and Mary had died in the years between Daniel's death and Patrick's death.) Catherine's obituary said that she had been born in Killcooler, Ire.
Another person in our group located Dingle, as being part of Kerry County. I had had success before with a Kerry County family using Irish Genealogy, a free web site with transcribed church records from Kerry County; as well as Carlow, Cork and Dublin. I went back to the site and located the possible birth/baptismal record for Patrick Moran of Killcooly. It seemed to match the information we had gathered, although the birth month was different from the one on the Naturalization Index Card we had found. I also found possible Baptismal records for Daniel, Catherine and Mary Moran of Kilcooley and a marriage record for their parents on this site in the Parish of Ballyferriter, in County Kerry. It appeared we had located the place of Patrick's birth in just a matter of minutes after finding the death record of his brother Daniel.
Much of the remaining part of that afternoon was spent on the County Kerry Genealogy website where we read about the civil and Roman Catholic parish divisions in County Kerry, and gained some knowledge of the history and geography of the area.
We almost certainly had found the homeland location, but our research was not finished ...