I believe that onboard audio continues to improve, but it is entirely possible that your onboard audio does suck. When I went from onboard audio in an HP desktop back in 2004 to a Creative soundcard, it was a huge improvement. I wouldn't count out a soundcard if I were you. You should be able to easily get improved audio for much less than $200 by going that route.
As for an external DAC, you would certainly need to connect a digital audio signal from the computer to the DAC. After all, that's what digital-to-audio conversion is all about.

Does you computer have a digital audio output (either optical or coax)?