Q: Error 3194 with iOS 7.0.4 restoring

That is not supportd by Apple. You have to restore to the latest iOS version for your model iPod. That is 7.1.1 for the 5G iPod.

The verison of iTunes has not effect.

It is not supported by Apple.

As I said n my first reply: "You have to restore to the latest iOS version for your model iPod. That is 7.1.1 for the 5G iPod."

If you try an earlier you will get the 3194 error.

Jailbreaking, including restoring to other than the latest iOS version for  your model iPod voids the Apple warranty and also means that you will not get any support from Apple, including from this Apple forum. Jailbreaking can't be discussed in this Apple forum.

Unauthorized modification of iOS has been a major source of instability, disruption of services, and other issues

Downgrading or modifying your iOS version is not supported and therefore can't be discussed here, sorry.

You can ONLY restore to the latest version, which is currently 7.1.1.

Not good.

Check for hardware issues

Related errors: 1, 3, 10, 11, 12, 13, 14, 16, 20, 21, 23, 26, 27, 28, 29, 34, 35, 36, 37, 40, 1000, 1002, 1004, 1011, 1012, 1014, 1667, or 1669.

Try to restore your iOS device two more times while connected with a cable, computer, and network you know are good. Also, confirm your security software and settings are allowing communication between your device and update servers. If you still see the error message when you update or restore, contact Apple support.