I placed a check at Crop to Rectangle in the shapefile object dialog box and set the crop rectangle to my area of interest, but now none of the shapes are being drawn -- in or outside of the rectangle.
Each shapefile consists of multiple shape objects. EnviroInsite processes these one at a time. If you have selected the Crop to Rectangle option then when processing a particular shape EnviroInsite checks each point of that shape. If all of the points are within the rectangle then the shape is drawn. If the shape crosses the rectangle boundary or is totally outside of the rectangle then the shape is not drawn.
In your case, you have drawn your rectangle such that none of the shapes in your shapefile are entirely within the rectangle. Try expanding the rectangle so that it includes the entirety of the shapes within your shapefile that are in your area of interest. That will exclude the shapes outside of your rectangle that you don't want drawn, while including the shapes within the rectangle.