So the answer was a whole lot further off base than I would ever have thought.
So I was using a somewhat trusty program called SRS Audio Sandbox (more recently SRS HD Lab or something) to adjust for the fact that my speakers kinda suck. Well, it doesn't work on audio cards that aren't connected to PCI (for some reason), so I uninstalled it.
Unfortunately, the installer did not remove the "Audio Filter" pseudo sound card that's used to capture your sound for processing (I guess it was in an error state?), so Device Manager listed it as working fine, but in the Sound control panel it was basically non-functional.
Apparently, having a sound card that refuses to fully initialize (or gets stuck, whatever) doesn't completely stop Windows from playing sounds, or using your functioning sound hardware, but it will screw up the UI for some reason.
Once I removed the broken sound card using Device Manager, all is well in the world, media keys work and the sound slider pops up when appropriate.
Who'da thunk it?