IPhone 5 keeps on turning off even in DFU Mode

I'm not really sure if we are in the same boat. I had been stuck in DFU mode after restoring my iPad to iOS 6.1 without activating it. I have tried using iTunes in restoring the firmware but it was stuck on the iTunes and usb logo just like you. What I did was to use redsn0w to restore my iPad. You can use it without jailbreaking your phone. Hope this helps.

This may seem silly, but this is what I do when I have had to troubleshoot DFU mode (getting in and out of). First cross your fingers that it is software. Do you have a different USB cable that you can try with? Access to another computer to attempt with. I'm sure you have already tried rebooting both the iPhone and Mac, right? Not sure if you know or not, but you actually don't the computer nor the cable to get in DFU. You may want to try without plugging it in as well. The only difficult part with that is since it is not plugged in you will not know when it boots into DFU mode until you plug it in and the computer chimes. These seem basic but even the best of us forget about switching ports, rebooting the computer or trying another cable.