There may be a problem with your zipped shapefile. Have you included all the necessary files in the zipped file? Shapefiles have many auxiliary files. Also, to import a CSV, you need to have the x,y locations of the points in the file as well. We look for field names like lat, long, x, y...
If these don't help, upload your zip file here and we can take a look at it.
Thanks,
Mike