After installing Blender and launching it, I noticed a console popup with errors that goes away shortly, followed by the program opening seemingly fine.
I didn't have time to read those errors so I hit my Shadowplay Instant Replay recording hotkey. Upon playback, I could read it. (Here's a screenshot:)

It got weird fast, because then I could hear in my Shadowplay recording, for the first time ever, a radio signal.
This happens with different microphones, too, including having no microphone in, so it's not a hardware issue! What could I do to fix my microphone input? I've since uninstalled Blender and am frustrated to have a problematic microphone channel on my computer now.
UPDATE: After uninstalling and reinstalling Blender, and also doing the same with the OpenAL library that seems to be related, I'm still having radio recorded on my mic channel.
UPDATE: It seems to stop happening temporarily sometimes. Haven't figured out the pattern.