As I said a few posts earlier, you can use a streamer to retrieve your iTunes music from your computer and send it to your stereo system. Effectively, this would replace your iPod.
To access the music stored on your computer (in iTunes), your computer and the streamer must be connected to the same local data network. If your computer has a high-speed connection to the Internet, you almost certainly have a local data network, whether you know it or not.
A streamer can connect to that network and access music stored on the other devices which are also connected to that network. Such as your computer.
I cannot imagine why you are so averse to taking advantage of the vast variety of music available via the Internet (the "GD cloud"). Do you understand that a streamer can access both the Internet AND the iTunes music stored on your computer? So if you don't want to use the cloud, you don't have to do so. Either way, the music stored on your PC stays on your PC.
On a related note; you are using the cloud to participate on this forum. And you used it to get your music from Napster.
As for connecting your dock to a DAC; I'll ask again - what kind of dock is it? Brand? Model? If it is an Apple dock, the answer is a hard no. There were a few docks made by other companies with the ability to extract digital output from an iPod, but they were not common.
What type of files do you have loaded into iTunes? If they are compressed (AAC), then an external DAC is not likely to be an improvement over the DAC built into your iPod anyway. And if you got that music from Napster, they are surely compressed.
If you decide to use a streamer, it can connect to your local network wirelessly (Wi-Fi) or physically (Ethernet), and connect to your stereo system via RCA jacks, same as your tape deck, CD player, etc. The Wiim Pro and Wiim Pro Plus are two excellent, and relatively inexpensive, choices for a streamer.
You would also need a device to use as a "remote control" for the streamer. Most people use their smartphone or a tablet. You could also use your PC, but that's not very practical in your situation since it is in another room. In any case, whatever you use to control the streamer must be able to access the same network to which the streamer is connected (for example, your home's wifi network).