Adding a splash screen to my java game

Ok here smy code at the moment for my game class:::
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import java.awt.*;
import java.awt.event.*;
import java.awt.* ;
import java.awt.event.* ;
import java.awt.image.* ;
import javax.imageio.* ;
import java.io.* ;
import javax.swing.* ;

public class JaySnake extends JFrame
{
  class Game extends JPanel implements Runnable
  {
    private BufferedImage backBuffer ;
    private Graphics myBackBuffer ;

    public Game()
    {

      /******Try read in backgroundImage file and catch any exception*/
      try
      {
        backgroundImage = ImageIO.read( new File( "default.jpg" ) );
        backgroundImage = ImageIO.read( new File( "blueGlass.jpg" ) );
        backgroundImage = ImageIO.read( new File( "grassBack.jpg" ) );
        backgroundImage = ImageIO.read( new File( "sand.jpg" ) );
      }
      catch( IOException e )
      {
        System.out.println( "Cannot load image file!" ) ;
      }
      backBuffer = new BufferedImage( DISPLAY_W, DISPLAY_H, BufferedImage.TYPE_INT_RGB ) ;
      myBackBuffer = backBuffer.getGraphics() ;

//set up the menubar
      menubar = new JMenuBar();
      setJMenuBar(menubar);

    }

    long startTime, waitTime, elapsedTime ;
    public void paintComponent( Graphics g )
    {
      g.drawImage( backBuffer, DISPLAY_X, DISPLAY_Y, null ) ;
    }

    public void run()
    {
      //     1000/25 Frames Per Second = 40millisecond delay
      int delayTime = 1000 / 25 ;

      Thread thisThread = Thread.currentThread() ;
      while( running )
      {
        startTime = System.currentTimeMillis() ;
        // render to back buffer now
        render( myBackBuffer ) ;

        repaint() ;
        //  handle frame rate
        elapsedTime = System.currentTimeMillis() - startTime ;
        waitTime = Math.max( delayTime - elapsedTime, 5 ) ;

        try
        {
          Thread.sleep( waitTime ) ;
        }
        catch( InterruptedException e )
        {}
      }
      System.out.println( "Program Exited" ) ;
    }

   
  }

  private Thread gamePlay ;
  private boolean running = true ;
  private Game game ;

  private final int DISPLAY_X ; // value assigned in constructor
  private final int DISPLAY_Y ; // value assigned in constructor

  private static final int DISPLAY_W = 600 ;
  private static final int DISPLAY_H = 600 ;

  int size, hsize = 0, score1 = 0, score2 = 0, highscore = 0 ;

  /****Creates JMenuBar */
  private JMenuBar menubar ;
  /****Creates JMenu to house items */
  private JMenu gameMenu = new JMenu( "Game" ) ;
  private JMenuItem gameStart = new JMenuItem( "Start" ) ;
  private JMenuItem gameQuit = new JMenuItem( "Quit" ) ;

  private JMenu bgMenu = new JMenu( "Backgrounds" ) ;
  private ButtonGroup bgGroup = new ButtonGroup() ;
  private JRadioButtonMenuItem bg1 = new JRadioButtonMenuItem( "Default" ) ;
  private JRadioButtonMenuItem bg2 = new JRadioButtonMenuItem( "Long grass" ) ;
  private JRadioButtonMenuItem bg3 = new JRadioButtonMenuItem( "Yellow Sand" ) ;
  private JRadioButtonMenuItem bg4 = new JRadioButtonMenuItem( "Blue Glass" ) ;

  private JMenu soundMenu = new JMenu( "Enable sounds" ) ;
  private JCheckBoxMenuItem soundMusic = new JCheckBoxMenuItem( "Music" ) ;
  private JCheckBoxMenuItem soundSound = new JCheckBoxMenuItem( "Sounds" ) ;

  private JMenu helpMenu = new JMenu( "Help" ) ;
  private JMenuItem userInstruct = new JMenuItem( "User Instructions" ) ;
  private JMenuItem helpAbout = new JMenuItem( "About" ) ;

  /******JaySnake constructor*/
  public JaySnake()
  {
    /*****Sets title for main window*/
    //setTitle("JaySnake Game");
    //getContentPane().setLayout( new BorderLayout() ) ;
    //setResizable( false ) ;
    //Causes Menu Titles to not show up when un commented
    //setIgnoreRepaint( true ) ;
    game = new Game() ;
    getContentPane().add( game, BorderLayout.CENTER ) ;
    this.setJMenuBar( menubar );

    menubar.add( gameMenu ) ;
    gameMenu.add( gameStart ) ;
    gameMenu.add( gameQuit ) ;

    // ActionListener to quit the game when quit is clicked
    gameQuit.addActionListener( new ActionListener(){  
   
               public void actionPerformed( ActionEvent e )
     {
        System.exit( 0 );
     }
      } ) ;                                                  
                         
    menubar.add( bgMenu ) ;
    bgMenu.add( bg1 ) ;
    bgMenu.add( bg2 ) ;
    bgMenu.add( bg3 ) ;
    bgMenu.add( bg4 ) ;

    bgGroup.add( bg1 ) ;
    bgGroup.add( bg2 ) ;
    bgGroup.add( bg3 ) ;
    bgGroup.add( bg4 ) ;

    menubar.add( soundMenu ) ;
    soundMenu.add( soundMusic ) ;
    soundMenu.add( soundSound ) ;

    menubar.add( helpMenu ) ;
    helpMenu.add( userInstruct ) ;
    helpMenu.add( helpAbout ) ;

    addWindowListener( new WindowAdapter()
    {
      public void windowClosing( WindowEvent e )
      {
        dispose();
        System.exit( 0 ) ;
      }
    } ) ;

    Insets insets = getInsets() ;
    DISPLAY_X = insets.left ;
    DISPLAY_Y = insets.top ;
    resizeToInternalSize( DISPLAY_W, DISPLAY_H ) ;
  }

  public void resizeToInternalSize( int internalWidth, int internalHeight )
  {
    Insets insets = getInsets() ;
    final int newWidth = internalWidth + insets.left + insets.right ;
    final int newHeight = internalHeight + insets.top + insets.bottom ;

    Runnable resize = new Runnable()
    {
      public void run()
      {
        setSize( newWidth, newHeight ) ;
      }
    } ;

    if( !SwingUtilities.isEventDispatchThread() )
    {
      try
      {
        SwingUtilities.invokeAndWait( resize ) ;
      }
      catch( Exception e )
      {}
    }
    else
      resize.run() ;

    validate() ;
  }

  public void start()
  {
    Thread gamePlay = new Thread( game ) ;
    gamePlay.start() ;
  }

  public static void main( String args[] )
  {
    System.out.println( "Starting JaySnake..." ) ;
    JaySnake app = new JaySnake() ;
    app.setSize( DISPLAY_W, DISPLAY_H ) ;
    app.setTitle( "JaySnake Game" ) ;
    app.setVisible( true ) ;
    app.start() ;
  }

/*Render method for graphics content*/
    public void render( Graphics g )
    {
     if( backgroundImage != null )
        g.drawImage( backgroundImage, 0, 0, this ) ;

      /******Draw scoreboard and player details, sets color for score and player
       ******draws rectangle in same green, draws strings and used variables score1
       ******and score2. Sets color again to black draws another rectangle
       ******that is used to highlight the playing area*/
      g.setColor( Color.green ) ;
      g.drawRect( 1, 0, 598, 32 ) ;
      g.drawString( "Player 1 score: " + score1, 10, 13 ) ;
      g.drawString( "Player 2 score: " + score2, 10, 27 ) ;
      g.drawString( "High score: " + highscore, 510, 15 ) ;
      g.setColor( Color.black ) ;
      g.drawRect( 1, 34, 598, 521 ) ;
     
    }

  /******declared class variables/containers*/
  private Image backgroundImage ;
}


Now here is a class that I have that creates a Splash screen without any borders on the Window.
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class Splash extends JWindow       {
       public Splash(String filename, Frame f, int waitTime)
             {
                 super(f);
                 JLabel l = new JLabel(new ImageIcon("splash.gif"));
                 //JLabel l = new JLabel(new ImageIcon("splash.jpg"));
                 getContentPane().add(l, BorderLayout.CENTER);
                 pack();
                 
                 Dimension screenSize =
                   Toolkit.getDefaultToolkit().getScreenSize();
                 Dimension labelSize = l.getPreferredSize();
                 setLocation(screenSize.width/2 - (labelSize.width/2),
                       screenSize.height/2 - (labelSize.height/2));
                 
                 addMouseListener(new MouseAdapter()
                     {
                         public void mousePressed(MouseEvent e)
                         {
                             setVisible(false);
                             dispose();
                         }
                     });
                     
                 final int pause = waitTime = 3000;
           
                 Runnable waitRunner = new Runnable()
               {
                         public void run()
                         {
                             try
                                 {
                                     Thread.sleep(pause);
                                     setVisible(false);
                                     System.out.println("Setting Visable");
                                       dispose();
                                 }
                             catch(Exception e)
                                 {
                               e.printStackTrace();
                                     // can catch InvocationTargetException
                                     // can catch InterruptedException
                                 }
                         }
                     };
                     
                 setVisible(true);
                 Thread splashThread = new Thread(waitRunner, "SplashThread");
                 splashThread.start();
             }
   }

Now what I want to do is to have the splash screen appear before my window loads up and I want to be able to click on the splash screen that will have the effect of loading up my game window.   Any ideas?  

I need to use the class in my game - How should I do it?

Thanks guys!