Internet connection does not work with an IP address space of 169.254.xxx.xxx from ISP, router, or manual configuration

Your Mac, iOS device, or Apple TV cannot access the Internet with an IP address of 169.254.xxx.xxx (where xxx represents a number from 0 to 255).   The symptoms of this issue include: Safari, iChat, and other Internet-dependent applications in Mac OS X may display the message "You are not connected to the Internet." Mail may put all of your email accounts into an "Offline" status. iOS devices cannot use other Internet features, such as the App Store. Apple TV may be able to use Home Sharing with computers on your local network, but not any features that require Internet access, such as movie trailers or rentals. In Mac OS X, an AirPort menu bar icon with an exclamation point may appear, and the AirPort menu may state "Alert: No Internet Connection…".   Use this article if: Your Mac, iOS device, or Apple TV is connected to a network that should provide access to the Internet, and which has a functioning DHCP server (such as an AirPort base station in default configuration). Your Mac, iOS device, or Apple TV is assigned an IP address of 169.254.xxx.xxx by your DHCP server, or you have manually assigned it an IP address of 169.256.xxx.xxx. Your Internet-facing router is being assigned an IP address of 169.254.xxx.xxx by your ISP.