With Soc Sec number it will be easier and a couple of bucks cheaper, to obtain a copy of the application filled out by the holder of that number.It should show the names of holder's parents, holder's residence at the time of application, and other data, too.
Our ancestors generated many more records then we often realize.Land, tax, probate, court etc.I suggest to check around, see if there is a Family History Center near you, and/or a local genealogical group.Help from others is always beneficial, saves you spinning wheels.
Post queries on your family on the surname forums, and the state and county forums, too.Be sure to include names, dates, or approximate dates, and locations.For example you may have the names of your great grandparents, but no dates on them.Then include names and dates of births (and locations if you know) for any of their children.This will put them in a time frame and location.
Have you used FamilySearch, the LDS site?Their version of the 1880 census is very user friendly. It includes an everyname index, too.
Have you used GenWeb sites?If not, let me know I'll give you some hints for them.They are different then GenForum.