Your downloaded shapefile already had a coordinate system defined in its *.prj file:

> PROJCS["NAD_1983_StatePlane_Texas_South_Central_FIPS_4204_Feet",GEOGCS["GCS_North_American_1983",DATUM["D_North_American_1983",SPHEROID["GRS_1980",6378137.0,298.257222101]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Lambert_Conformal_Conic"],PARAMETER["False_Easting",1968500.0],PARAMETER["False_Northing",13123333.33333333],PARAMETER["Central_Meridian",-99.0],PARAMETER["Standard_Parallel_1",28.38333333333333],PARAMETER["Standard_Parallel_2",30.28333333333334],PARAMETER["Latitude_Of_Origin",27.83333333333333],UNIT["Foot_US",0.3048006096012192]]

You appear to have used **[Define Projection][1]** to change how the coordinate values (which are in feet) get interpreted (as meters).  This does NOT project the coordinates.

I recommend that you try the **[Project tool][2]** instead.


  [1]: http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?id=1886&pid=1884&topicname=Define_Projection_%28Data_Management%29
  [2]: http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=project_%28data_management%29