Ethernet streaming and occasional white noise on Windows

[AlexS]

Is it possible that the screen server kicking in is just an indication that the computer is "idle", and that something else is configured to run under that condition (e.g. a virus scan)?

Yes, so I would first disable the screensaver (as @Confused was going to), to rule out/in this possibility, and then temporarily disable the anti-virus, if disabling the screensaver does not help.
I ran into a case where Windows Defender (kicking in when it thought my computer was idle, installing the latest definitions and running a scan) caused a stutter in JRiver playback. (Not white noise in my case, but @Confused did observe that his problem sometimes would manifest itself as a stutter).
If this turns out to be the anti-virus, there are instructions on how to make it JRiver friendly, on their forum.