Iโm not sure how you get any sound at all with the power cord unplugged. ๐
But we generally hear ground loops as a hum, except!! Digital ground loops. They are a real thing that can occur with USB or coaxial digital connectors.ย I have never heard of this causing more than excess jitter though.
Seriously though, it should be 100% illegal to sell a DAC that doesnโt have complete galvanic isolation for itโs digital inputs.