Projection files, which should be listed in the Coordinate Systems directory, do not display in the following locations:
ArcToolBox Define Projection Tool
ArcToolBox Project Tool
ArcMap > Display XY Data > Edit button > Select
ArcMap > Data Frame Properties > Coordinate System tab > Predefined folder
The check box labeled 'Coordinate Systems' located in ArcCatalog > Tools > Options > General tab, in the lower window has been unchecked.