Good, yes, it does seem as if you've isolated the problem to the Radio Shack cable. If you want to be sure that's the issue it might be worth it try a different cable, such as this one. The Monoprice cables are of excellent quality at reasonable prices and they ship the same day you order.
An external DAC would be the next step up and while I don't have any experience with the Dragonfly since I've always used the optical output on Macs, it has a great reputation.
An external DAC would be the next step up and while I don't have any experience with the Dragonfly since I've always used the optical output on Macs, it has a great reputation.