I've never not had a webcam working if the kernel sees it. What you could do is plug the webcam into the usb port and then run the following.
Then check what the output says, maybe it will display an error or something that we can work with. Did you check if other usb devices worked correctly just as a comparison? If other usb devices don't work either you could try resetting the usb controller.
After a long uptime specific (cheap) devices or components connected to the USB ports lock up or malfunction. Unplugging and plugging them usually fixes issues, but physical access to the system (especially a remote server) is neither always possible or desirable. In cases like this, Linux...
zedt.eu
You could have also tried a newer kernel to see if that would have give you different results since Debian isn't known for it's new packages. Maybe you shouldn't have gone for Debian but a distribution with newer packages and libraries? Maybe you should have a backup laptop with Windows in case you can't get something working, that way you won't always have to rely on forum topics when it could effect something import in real life?