IPod Touch 4g does not restore/update - error 3194

Question

Hello,
I've recently been having a great deal of trouble with my 64GB iPod Touch 4g, which I purchased in maybe late March or early April of this year. I consider myself adequately learned in technology and I've done a vast amount of research into this problem, and have not been able to resolve it, so I took it upon myself to ask my question here.
Firstly, I am running iTunes on a Windows 7 64-bit system, and I should note that I have found lots of answers to similar problems for people with jailbroken iPod Touches, but I don't think these solutions would work for me since I have not jailbroken my iPod. I have also not yet upgraded to iOS 6, but was on the latest version of iOS (5.x...I don't remember). Also, I bought my iPod from Amazon so obviously the 30-day return window has expired.
Anyway, on to the problem. Yesterday, my iPod froze and so I reverted to the 'hard reboot' method of fixing it by pressing the home key and the sleep key at the same time, and released when the Apple logo showed up. I waited for the device to reboot as it normally does, except that in all the previous times I have done this hard reboot, while the Apple logo shows up for a little while until the lock screen loads, this time that did not happen. Instead, there were colored bars that showed up on the screen (I don't know how to describe it, exactly) that eventually covered up the Apple logo and faded into a completely white screen. From this screen, I tried the hard reboot again and the Apple logo showed up again, only to be covered up by those bars and fading into white again. I tried rebooting it a few more times, but to no avail.
I then opened iTunes and plugged in my iPod, but it was not recognised by the computer (presumably because it was not fully on), so I tried putting the device in DFU recovery mode (hold the sleep key and home key until the device tells you to connect to iTunes). At this point, iTunes seemed to recognize that a device was plugged in, but not that it was my iPod because where it normally gives you the information (my iPod, Capacity: ...., Serial number: ... and so forth), the information just read 'iPod' (not 'My iPod', as it was named before this unfortunate event), 'Capacity: n/a, Serial number: n/a', and so forth. I pressed the 'restore' button and there was an error, 3194, on the step 'Verifying restore with Apple'.
So I went to Google, looking up troubleshooting tips for this particular error, and most of the answers I found were just for people with jailbroken iPods, even though mine isn't jailbroken. I have tried numerous solutions (updating the hosts file in drivers, turning off the firewall, etc) to no avail, and I still get that pesky white screen whenever I try to reboot my device.
I'm also worried that even if I get my device to restore successfully, then it still might not boot up properly. To be honest, I'm a little more worried about the booting problem than the restoring problem.
Does anyone have any advice for what I should do in this situation, other than visit the Apple store? There is one in my town but I feel like I've invested a lot in this device and I don't want to pay too much for any repairs that may need to be done (especially considering that this appears to be a software issue and not a hardware one); I'm a high school student and don't have that much money.
Thank you for any help.

Answer 1

See the actions for that error here:
iTunes: Specific update-and-restore error messages and advanced troubleshooting
Also
iPhone Error 3194 - How to Fix iTunes Error 3194?
Fix Error 3194 from iTunes during iPhone restore