I bought an XPS15 a few weeks ago and tried to use the webcam for the first time with Skype today, but it didn't work. I tried through the "Camera'App, but all I get is a black screen. I reinstalled the Driver, BIOS and chipset, but none of these solutions which I found on the Dell webpage worked. Running the diagnostic tool says the camera is working OK, but the detailed results tell a different story:
What is the exact system model? What is the current OS installed on the system? Is there any smudge or dirt near the camera? Have you placed any screen guard around the bezel? Is the camera detected fine in device manager under imaging devices?
Since you have already updated BIOS and state drivers have been replaced, then you have tried most possible options.