Lenovo T420 integrated camera is not working

I now it's rather late to post any answers here, but I just had the same problem and the solution is actually much less cumbersome than all the answers so far. The camera is in privacy mode (obviously it likes to change that by itself) and you can turn it back to normal by just clicking "show my video image" in the settings page visible on the screenshot posted in the question.

You get to this settings page by opening Lenovo - Web Conferencing.

had the same issue with the same configuration - t420, win 64bit, had the lenovo-suggested driver installed (and re-reinstalled) and camera wasn't working, with same behavior as described in your issue and picture.
for my case, an addition to the behavior described is: when i had the communication settings screen open (i.e. where the camera should appear but didn't), the camera's green Led was lit, suggesting it's started.

searched about it quite a bit, and finally now i did something simple - uninstalled camera from the device manager . refreshed the device manager and automatically the camera got reinstalled under the default Win driver. Ta Daaaaaa... camera's working now.
i guess it's not the top performance/quality that the manufacturer's driver should've offered, but... at least it works.

i don't know to what extent this trivial solution works on your case, nor if you tried it already, but hope it helps.
now i'm still curious what happens if i reinstall the lenovo camera driver. i'll try that too.

Check your Lenovo settings menu, go to camera settings, and make sure you are set to normal instead of private.