Q: Cannot Restore Apple TV (3rd Gen)

My problem began when I ran into the notorious problem of the Apple TV (3rd Gen) crashing after auto-installing the latest update. Specifically, ever since the update, it will only boot to the Apple logo. Rebooting simply returns it to the logo. I figured I might've been impatient, so I let it sit for a long while, only to come back maybe an hour later to find it still frozen on the logo.

So I tried to restore it to factory settings via iTunes, but this has led to my current problem -- Neither my PC (Win 7) nor iTunes will recognize the device.  I followed the standard 3rd gen method of connecting: Connect via micro USB (data cable, not charge cable), connect power. It fails to appear in iTunes, device diagnostics show no devices connected, and Windows doesn't appear to even acknowledge its connection.  I've tried unplugging and replugging power and USB multiple times in different orders with no change in results. (Hilariously, for one brief moment, it did show up in iTunes -- as my iPhone!?)

I can verify power is working as I can see the optical port lit red when connected.

I seem to have hit a brick wall, and I'm almost certain this is a software problem (as opposed to bad hardware) given it crashed immediately after the update.

This is the USB cable I'm using: http://www.amazon.com/gp/product/B00JWPENRU/ref=oh_aui_detailpage_o01_s00?ie=UTF 8&psc=1