Conexión a SQL Server en ASP.NET

Creo que también debe crear un objeto de la clase SqlCommand y pasar la cadena de comando a su constructor. prueba esto"

SqlConnection conn = new SqlConnection("Data Source=serverName;"
           + "Initial Catalog=databaseName;"
           + "Persist Security Info=True;"
           + "User ID=userName;Password=password");

conn.Open();

// create a SqlCommand object for this connection
SqlCommand command = conn.CreateCommand();
command.CommandText = "Select * from tableName";
command.CommandType = CommandType.Text;

// execute the command that returns a SqlDataReader
SqlDataReader reader = command.ExecuteReader();

// display the results
while (reader.Read()) {
    //whatever you want to do.
}

// close the connection
reader.Close();
conn.Close();