You can try using the jQuery Cookie Plugin.
The cookie is a form of persistent storage. When a user loads the page, you check if he has a certain cookie. If he doesn't, you show him the splash page and set the cookie. If he has the cookie set that means he's been here before and you don't need to do anything. The following code could be a solution, but I'm writing it out of my head so you'd probably have to modify it a bit. It assumes you're using the plugin above.
if (visits = $.cookie('noOfVisits')) {
$.cookie('noOfVisits', visits++);
} else {
$.cookie('noOfVisits', 1);
$('#splash').show();
}
I think that it's pretty self explanatory. Note that the cookie expires, research how to make it last as long as you want.
Hope this helps :).