I tried what you said:
I copied the file you attached (wgs_84.prj.txt) into the folder with my shapefiles. I'm not sure, but I think wgs 84 is correct for central Illinois.
One in question is: Smith Mains.shp, Smith Mains.dbf and Smith Mains.shx
So, I renamed your file wgs_84.prj.txt to Smith Mains.prj and put it in the same folder.
When I tried to import that into ArgGIS Viewer I still got the same message that it didn't recognize the coordinate system.
Why doesn't ArcGIS recognize this problem? Why do they let you think you can load .shp files when you can't? Why don't they tell you all these little secrets in their Help menu? Why don't they have a pop up window with multiple choices for which projection system it is using? Where can I find a program that will do this correctly?