I think possibly this is just an OS X adaption issue. In OS X, running applications need not have any windows. If you launch Xcode with the intro screen disabled, it will launch with no windows. However, it will have a working menu bar. If you click Xcode in the Dock to activate that application, you should see the menu bar change to one that says "Xcode" in the top left of the screen next to the apple.
From there, click on File and New Project, or alternatively press shift+command+N to get to the screen you want.
Does that help, or is Xcode even failing to offer you its menu bar?