I get no sound / notification / whatsoever, when I plug the board in. I have tried 3 PC's and different USB ports but still nothing. There's no "Arduino Uno" or "Unknown device" in the hardware manager, either. However, the "ON"-led on the board lights up and the "L"-led starts blinking.
--_: There's no "Arduino Uno" or "Unknown device" in the hardware manager, either.
It's not the "Arduino itself" that connects to your PC, it's the FTDI serial to USB brigde that should show up somewhere as "USB to serial adapter", "FDTI [...]" or "Future Technologies Devices [...]".
Anyhow, did you try uploading one of the examples with the Arduino software?
You can also check Windows' available COM-Ports - there should be an additional one after you plugged your Arduino in.
There is nothing like that in the Device Manager. In fact, nothing changes in the Device manager when I plug the Arduino in (yes, I did refresh). There's really no indication of the Arduino or 16u2 on the PC.
Edit. I also ran usbdeview while plugging the UNO in and it didn't show any new USB devices.
Judging by your information so far, this is quite unlikely to work, but please try it anyway:
Try uploading e.g. the "Blink"-Example ("Files"->"Example"->"01.Basics"->"Blink") with the Arduino IDE. If there are error messages, try changing the serial port to all the different ports listed under "Tools"=>"Serial Port" before each upload.
If that doesn't work, I'd try to use an other USB cable, if that doesn't work either there's probably a hardware issue with your Arduino.