Can you confirm that the shapefile includes identical files with the following extensions? .shp, .shx, and.dbf?
If so, then it should show up if not corrupted. But is there a chance thar your .prj is the wrong projection? Happens when using define projection tool to change projection. For example, perhaps the shapefile is a a geographic coordinate system however the projection file says it is in Web Mercator? That kind of mismatch in projections will result in it not displaying.
Lastly, if all of these don't work then perhaps also delete the .sbn and .sbx files (that store the spatial index) as I have had trouble with them before being corrupted. But in these cases, if you zoom out far enough the points do show. But do first back them up.
From your screengrab I cannot tell what the shapefile extensions were as you are hiding the file name extensions. You should change these in Windows Explorer from the View tab.