For this research, I started with James as there was a clear place/year of death in South Dakota. Dan was born in 1925 in SD, but no information as to where he might have died. The 1930 Census only had one Dan* O'Connell in SD, also having a father James, so he could have been found easily without asking for more information on him.
South Dakota Death Index:
James L. O'Connell died in Pennington County on 12/31/1957
His gravestone, 1885-1957:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=o&...
The stone and obituary of his wife, Doris:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=o&...
--SD Marriage records show marriage to James Lewis O'Connell on Jan 14, 1914 in Stanley, not 12/30/1913 as identified in the obit; but this date "might" be the date of recording.
I found a page in the book: "Midland Community..." that has a short bio on James and Doris. I copied it but can't send without your email address. Click on my name on the top left corner of this posting to obtain my email address, send me an email and I'll send the page to you. It is in jpeg format.
The 1930 Census for Township 4, Pennington Co, SD
James O'Connell, 44, born in South Dakota to both parents born in the US, farmer/stock farm, owned his land, first married age 27
Dorris(as written), 44, born in Iowa to father born in Ohio, mother in IA
Mary, 15, SD
Freboria(?), dau, age 13, SD
James, 11, SD
Warren, 9, SD
Winifred, 9, SD (Twin to Warren)
Colin, 7, SD
Merle(as written, probably Muriel), dau, 4 6/12
Dan, 4 6/12 (Twin to Merle[Muriel])
--Census enumerated April 23, so Merle(Muriel) and Dan born about Nov 1925
--Cemetery information re: Daniel Ledger O'Connell, 11/25/1925-6/12/2007http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=o&...
--This "might" be the cemetery information of James:http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSln=o&...
The 1900 Census for Orland, Lake County, SD
-William F. O'Connell, born Nov 1853 in Vermont to both parents born in Ireland, Farmer/Renting his land, married 22 years.
-Ellen, 44, born Feb 1856 in Wisconsin to both parents born in Ireland, mother of 10/10 living.
-Daniel P, Dec 1879, WI
John C, Aug 1881, SD
Willie H, Feb 1883, Wisconsin
James S(probably an L), born Sep 1884, SD
Anna, Nov 1885, SD
Mary E, Sep 1887
Lawrence F, Feb 1889
Charles E, Dec 1890
Charlotte K, Dec 1892
Joseph F, April 1895.
--This confirms James was son of William, William born in Vermont.
The 1930 Census for Glasgow, Valley Co, MT
William F. O'Connell, age 76(1853/1854), born in Vermont to both parents born in the Irish Free State (IFS). Farmer/General Farm, Renting. First married age 24.
Ellen, age 73, born in Wisconsin to both parents born in the IFS. First married age 21.
Montana Death Index:
William O'Connell, born about 1854, died 27 Jan 1938.
Ellen, born about 1856, died 11 June 1943.
--The record did not identify location, your "Malta" is in Phillips County. Jordan, burial place of Ellen is in Phillips and Garfield.
The 1860 Census for Baraboo, Sauk County, Wisconsin
J(or Y) O'Connell, age 35(circa 1824/1825), laborer, born in Ireland
Ellen, 33(circa 1826/1827), born in Ireland
Ann, 9, born in Vermont
Wm, 7, born in Vermont
--While this meets basic criteria, born in Vermont, both parents born in Ireland, living in Wisconsin where William's wife was born, there is NO PROOF this is the correct person. The census was enumerated the 4th day of September, the "correct" William would have turned 7 in November. Census records are often wrong or having small errors.
Now then, your #1 listed was a Lawrence O'Connell. You identified an "O'Connell father (1857-1903)." But, if William was born in November 1853, he could not be his father. The correct father of William would have had to have been born at least 1835 or before. While the family found in the 1860 Census matches criteria for this age group, again, there is no proof this is the correct family.
"Family's oral history" It's usually filled with mistakes. I once did research for a woman that was ADAMENT that a family member died in one state...I later found them in another. This oral history could have started with the emigrant from Ireland's name was given to a son of William...and Lawrence became that name; while in fact the correct son was James (which might match the potential person found above). It is always best to document family lore... but then start by reviewing ACTUAL records.
Wisconsin Vital Records search: http://www.wisconsinhistory.org/vitalrecords/
--No findings matching criteria of marriage, births.
There is no "quick" route between William and his father due to factors:
Vermont: William born in Vermont, since there is no known location and year was 1853/1854, records of birth are probably incomplete/non-existent and would require a local Vermont researcher for help. What you'd need to do is post in Vermont unknown, paste the link to THIS posting as a background into the research; but also, type in the name of William and the date of birth data found.
Wisconsin: "IF" William's family did go to Wisconsin as found in the 1860 Census, research would be needed in that county to eliminate or verify. Again, post in that county, paste this link. William's wife was born in Wisconsin, but that does not mean they had married there; but it needs to be researched. They were in SD by the 1900 Census, but son Daniel was born in WI in 1879, then John was born in SD in 1881, then Willie was born in WI in 1883. This "indicates" they first went to SD between 1879 and 1881, then back to WI, possibly to visit Ellen's family/have the child. The birth record for Daniel and Willie might help locate the family in Wisconsin, possible place of marriage; but, records for that period of time are probably very incomplete. You will have to first post in Wisconsin/Unknown
South Dakota: Records for Lake County for William. Post in that county, again post link to this search. Records might include a bio published in a local book. In some cases, the person would have to write his own data and sometimes pay for publication.
Montana: You have the county and date of deaths. Attempt to obtain an obituary for each person. Obituaries are not written for every person, a family member or friend would have to pay for publication. If they didn't live in the area long for persons to know them, one might not be written. If they lived in a very rural area where there was no local newspaper, one might not have been written(as is possible in this case). Could they have gone to this area to live with one of their children? You will have to post in Phillips again with the full DOB, but since this is the Phillips County site, perhaps a local researcher can now help. BUT, I would suggest reposting and identify "William O'Connell in Phillips County" as your subject title. And, also identify full information as to location in the body of the post. You might also post in Valley County, as that was where they lived during the 1930 Census, with death only eight years later for William.
BUT, the search for William's father does not stop with William. Finding records of his other children might identify other clues.
You have a lot of research ahead. It is time consuming but enjoyable, especially if you do it yourself. Genealogy is like a crime scene and you are the detective searching for your Subject, guilty of being a family member. Look for any and all clues.