I'm the same boat. Yesterday my camera stopped working Both Microsoft and Lumia Camera. Any app that uses camera doesn't works also. I've already tried >Soft Reset >Hard Reset >Nokia Software Recovery Tool and none of this things worked. So sad. But if I open Lumia Camera and tap back, app won't close so I can select front facing camera and it works perfectly. I really don't want to send my Lumia to Nokia Care, as they don't have any replacement for now and I'll have to wait a looooong time to get it back.
I'll use Nokia Care Suite to test hardware if there's any flaw and I'll install an older version of 830 system pre-Denim. Maybe it is a corrupted firmware from Nokia (I've noticed some errors and small glitches with apps that use Camera API after Denim update). I'll reply it later today with the results.
EDIT: Nokia Care Suite can't set it to test mode (not available on WP8.1 Update1) and can't install an older software, tried to refurbish but camera still not working. I'll bring it to Nokia Care :\