I have found a difference between the old version of the shapefile that does add to the map and the version that I need to add to the map.
Both versions have the following file types: cpg, dbf, prj, qpj, shp, shx.
The file that is successfully adding to the map also has an shp.xml file, while the other file does not. I suspect that is the reason and perhaps I may just need to figure out how I generate that file type. I can't recall but I may have done it within ArcGIS by first exporting my shapefile to a geodatabase. I could be wrong but I vaguely remember doing something like with the older file in a random attempt to get this to work. We'll see how it goes.