Well, now I've installed the Trends Audio 10.1 UD USB converter, in place of the no-name Chinese unit mentioned in my OP, and the computer is still generating the exact same pops and clicks. Could it be the buffer? BTW, the computer is a Dell Inspiron 8500 running Windows XP (2002 version).
The Trends may not be the "best equipment" either, but I don't think that is the issue, since it is reproducing the same problem that the prior USB converter was. And I've never heard anyone complain about the Trends causing this problem before.
For that matter, I've never found a post of anyone complaining about this particular issue with a USB converter, though I would not be surprised if they were out there.
In any case, I would surely appreciate your advice or other help.
Thanks as always.
BTW, the rest of the system is a set of Tekton Design single-driver speakers, Trends Audio amp, and Superpro DAC, which have always performed quite well together.