OK, as expected the another machine has a completely different codec (Realtek), and this works easily. OTOH, this one, Alienware Area 51-R2, has Creative CA0132 codec, and this is known to work only on limited machines, unfortunately. You can find many bug reports regarding this on the net. A part of the reasons is that Creative did lots of vendor-specific extensions, and the binary firmware blob we have matches only to certain models. I guess yours doesn't. Some Alienware models seem working with minor adjustment, and my patches does apply to your model. Alas, it doesn't seem working. That said, currently your new hardware isn't supported by upstream, mostly due to the reason above. You can try the latest kernel in OBS Kernel:stable, but I bet it won't work, either. Currently there is little hope for this kind of devices, unfortunately. One remaining question is: did you try the output from the headphone jack? When you plug there, try to toggles some mixer switches appearing in "alsamixer -c0". CA0132 chip doesn't support the simultaneous outputs from both headphone and others, and this is switched via the mixer switch.