DAC's and external portable hard drives

Please provide some more information. Does your computer have a wi-fi signal that will reach the media/audio room? What software do you use to play the music on the computer? What inputs does your DAC have, USB, optical, SPDIF, etc.? What's your budget?

If your DAC has an optical input the cheapest, simplest way to make a connection might be to buy a used Airport Express or Apple TV, one of the previous models that have the combined optical/audio output. Put either one on your network and situated next to your DAC. Then use a Toslink to mini-Toslink cable or a Toslink cable with a mini adapter to plug into your DAC, select the Airport Express or Apple TV as an output in System Preferences and then in iTunes. select an album or playlist and hit play.
It isn't going to be the best in fidelity but it's an inexpensive proof of concept.