I figured out where the sound was coming from. Arrrgh.
It was some type of alert beep being generated by Windows 7 through my remote desktop connection. This is a clear case of Microsoft trying to be smarter than its customers, since I had already made sure to turn off every single sound in the Sound control panel. Apparently MS thinks I mean every sound except whichever they still feel like making.
The only solution I've been able to come up with is to turn off sound in the remote desktop client. I happened to chance upon this as I must have hit shift a few times and caused the accessibility request window to come up which played the beeps. However yesterday there were no windows or visual warnings coming up along with the sound that I could see. At least if there were, they were transient and short-lived at that, so when I would flip back to RDC I wouldn't see anything.
Windows 7 wasn't my idea, and I'm not a piece of hardware or a product. Worst ads ever.