Neither Firefox nor Chromium detect my webcam and microphone on my desktop computer, although Skype does.

I have Skype 4.3 on openSUSE 13.1 on my desktop. It detects and uses my webcam (CIF Single Chip from Pixart Imaging, 093a:2471, badged as Genius VideoCam Ge111) and generic corded headset with microphone, so the hardware is known to work.

Firefox 33.0 and Chromium 37.0, however, detect neither webcam nor microphone. Using https://appear.in/ in Firefox to test, I create a room and a Firefox dialog appears asking if I want to share my camera and microphone with appear.in. The dialog lists my webcam and audio by name. I accept, but nonetheless the website responds with "failed to get camera and microphone access".

I'm using Firefox and appear.in as examples; Chromium, and other websites that use WebRTC to access the webcam and microphone, behave similarly.

This only happens on my desktop. On my notebook with built-in webcam and microphone but same OS and browsers, all works as expected. Searching the web didn't turn up anything, so at this point I'm stumped. Ideas?