If I understand you correctly, you're not sure how to make the extended splash screen (splash.html) disappear and have the content in default.html appear, correct?
The key thing is how the extended splash screen is dismissed and how you get the app home page to show--the MSDN tutorial isn't particularly good at pointing out how this works.
There are two ways to approach the implementation here.
One is to have the content for your extended splash screen AND your app's home page as sibling elements in default.html, like this:
<body>
<div id="mainContent">
<h1>This is the real start page</h1>
<p>Other content goes here.</p>
</div>
<!-- This div (declared last) will overlay the rest of the page initially; the elements within it will be
repositioned according to the default splash screen layout, then animated or shown. -->
<div id="splashScreen">
<p><span id="counter"></span></p>
<img id="logo" src="/images/splashscreen.png" />
<img id="title" src="/images/splashscreentitle.png" />
<progress id="progress" class="win-ring win-large"></progress>
</div>
</body>
Because the second div overlays the first, that's the content that will be visible as the extended splash screen. When it's time to remove that splash screen, you can make that element hidden (as you are doing) or remove it entirely from the DOM (to free memory).
The second approach is to use page controls, where default.html hosts the PageControlNavigator and the first page to which you navigate is the extended splash screen page. When it's done its work, it then navigates to the app home page. (In this case, set WinJS.Navigation.history.current.initialPlaceholder to true beforehand if you want to not have the splash screen in the history, see my blog on http://kraigbrockschmidt.com/blog/?p=741.)
In your code, I see that you're using the navigator already, but I don't think it's doing what you want.
The bottom line is that you somehow have to navigate from splash.html to default.html, and I don't see where in your code you're doing anything like that. This is why having the ext. splash screen as part of default.html makes good sense, and I find that an easier way than trying to navigate page controls for this purpose. I have an ExtendedSplashScreen example in the preview of my second edition book (http://aka.ms/BrockschmidtBook2), Chapter 3 (but will be in an appendix in the upcoming second preview), that does this.