MacBook – Built-in Webcam working only in 1 app and not in others (15” MBP, non-retina, mid 2012)

I have a MBP 15'' (late 2012; bought in June 2013) and I've noticed that the built-in Webcam doesn't work – except with Cisco WebMeeting!!

I had recently opened the laptop to change the HD, so I thought I had touched the camera connection, or something — but then I found the camera works in one app!!

The issues:

• Trying to use the WebCam to get pictures/video from any of the "usual" suspects says "there is no built-in camera available".
• I've tried with may applications:
  • Snag-It ("Capture -> New Image Capture -> Webcam"): The app goes into "capture" mode but nothing happens
  • Evernote (File -> New FaceTime Camera Note): I get a Black "preview" screen that says "Evernote Couldn't find a Webcam"
  • FaceTime: I get a black window with a "crossed out" icon of a camera
  • PhotoBooth: A different window, with the same crossed out icon, and a message "there is no connected camera":

Checking in System Information, I can see the camera listed so it's not a "hardware not connected" problem:

So imagine my shock when mucking about in a Webex, I noticed the "camera" icon and I clicked it, thinking that it wouldn't work, and the result was:

(I've blurred my ugly mug in the picture to protect the sensibility of innocent bystanders!)

So, any hints of what might be the issue??