Sorry to tell you your dedicated GPU failed. Went you are running single user mode you're using the built-in graphics services of the CPU (Intel's Iris graphics). During the bootup cycle the dedicated GPU is enabled which is why it fails to finish booting.
Apple has a recall on this issue which you might be able to sneak in on depending on where you live. If you live in the UK then you have a small window here to get the logic board replaced under extended warranty otherwise it's a new logic board or finding someone who can fix your logic board if they can.
Make your way to an Apple Store ASAP! Let them fix this under the extended warranty.