First thing I tried, actually - once the bug hit, I tried switching to mouse controls (bog standard microsoft wireless mouse here, too), and they were behaving in exactly the same way. If you load my save, you won't get any control response (except for camera turning) whether you're using mouse or gamepad.
Yes, I didn't get any control response with your save as well.
What I am wondering is: does the issue occur if you start a clean save (as in one that you still have controls) with mouse? I'm not suggesting to use kb/m with your uploaded save file since it is pretty much screwed.
The logic behind this is: the problem might be caused by specific hardware drivers that somehow triggered an infinite loop (i.e. doesn't read your input at all) which is broken by some interrupt (like what sporati suggested, e.g. getting hit). Assuming that is the case, if the infinite loop has already been running (and saved), changing your input device might not help. Which is ultimately why I suggested starting a new game / clean save with kb/m to see if you experience the same issues.