Any update on this? I have this exact problem. No unlock, not root just pure OTA stock.
1. Video does not record. You press the red button and no timer comes up.
2. A VID_20140126_224910.mp4.tmp file is created 395.54 KB.
3. Time lapse works as do all the other camera functions.
4. The basic Google FAQ has generic instructions if an app does not work so I followed these.
5. in safe mode the camera works fine.
6. Power off and on again. The Video Camera then works fine and creates normal .mp4 files.
Things I have done that may affected the Camera in the first place;
1. Clear cache.
2. Put a .thumbnails file in DCIM to stop the gigantic .thumbnail folder being created.
3. Running nova launcher.
Unlikely these are a factor as I isolated them as an issue and rebooted but worth a mention just in case.
Camera works but have found the it subsequently stopped working again and had to repeat the Google FAQ steps to fix an app.