What your code does is show the menu only when the the button has been clicked, but only for that frame. You need to set a variable when the button is clicked, then check every frame if the variable has been set, and draw the menu if it has. Something like this should work (untested):

var customButton : GUIStyle;
var windowRect : Rect = Rect (20, 20, 120, 50);
var showMenu : System.bool = false;

function OnGUI () { 
    if (GUI.Button (Rect (1195, 6, 70, 20), "Menu", customButton)) {
        showMenu = true;
    }
    if (showMenu) {
        Menu();
    }
}

function WindowFunction (windowID : int) {
    // Draw any Controls inside the window here
}

function Menu () {
    windowRect = GUI.Window (0, windowRect, WindowFunction, "My Window");
}

I tried this and my script and this line,

var showMenu : System.bool = false;

wanted to be.

var showMenu : System.Boolean = false;

-kenm

try this it might help you out.

http://www.youtube.com/watch?v=YtBegzGYyjc&feature=channel