In AutoCAD did you try using a data connection to the shapefile? From the Data Connect window click on add data connection, there should be an option in the list to add a shapefile. Since all the contents of your shapefile is in one file location you should be able to connect to the shapefile. You will then be asked to set the projection for the shapefile if there is no projection file present. If there is a .prj file it will automatically detect the projection, otherwise you will need to select the projection from the drop down list. After this click add to map to add the contents of the map to AutoCAD. If you want to save the contents of the shapefile in a DWG, you can select all the features, right click and click on check out data. Then right click and click extract geometry from features. This will extract geometry from all the features to line work in AutoCAD format. You can then right click and click check in features to save the shapefile as it was. You can remove the data connection and your line work of the geometry will remain as is.
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