When you say that it will not start but it is there in the dock, does the Scrivener menu appear at the top of the screen? If so, you need to go to File > New Project to create a project, or to Help > Tutorial to view the tutorial project. There is no application window to see until you have created a project.
In 1.1 and the new beta, to avoid this sort of confusion for new users, a dialogue appears upon first launching, asking the user if they would like to go through the tutorial, and explaining that if not, they need to go to File > New Project. In your case, though, because you only downloaded the beta after launching the other version, Scrivener recognised that it wasn’t your first ever launch so didn’t show the dialogue… Anyway, glad it’s up and running now.
To be honest I’m not a big fan of splash screens. They’re fine for programs such as Photoshop that require a lot of pre-loading, and so need to display something just so that you know they are alive, but for programs such as Scrivener which appear fairly quickly, they’re not so good: either the splash screen will disappear before you’ve had chance to look at it, or the splash screen has to slow down loading just so that you can see it.