What do you specify for the Data Source parameter in a C# connection string?

The following either returns a syntax errror or a runtime error:

Code:
"Data Source=.\SQLExpress;Initial Catalog=Chinook;Integrated Security=True;"

"Data Source=MYLOCAL-PC\SQLExpress;Initial Catalog=Chinook;Integrated Security=True;"

"Data Source=SQLExpress;Initial Catalog=Chinook;Integrated Security=True;"

"Data Source=MYLOCAL-PC;Initial Catalog=Chinook;Integrated Security=True;"

"Data Source=(local);Initial Catalog=Chinook;Integrated Security=True;"

The coding is as follows:

Code:
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
using System.Data.SqlClient;

namespace Example1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void Form1_Load(object sender, EventArgs e)
        {

        }

        private void btnAdd_Click(object sender, EventArgs e)
        {
            SqlConnection cs = new SqlConnection("Data Source=SQLExpress;Initial Catalog=ChinookPlay;Integrated Security=True;");
             cs.Open();
            MessageBox.Show(cs.State.ToString());
            cs.Close();
        }
    }
}
The run time error is:

Code:
  Message="A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server)"
  Source=".Net SqlClient Data Provider"
  ErrorCode=-2146232060
  Class=20
  LineNumber=0
  Number=53
  Server=""
  State=0
  StackTrace:
       at System.Data.SqlClient.SqlInternalConnection.OnError(SqlException exception, Boolean breakConnection)