There used to be an issue with AMD processors using only one core for AH while Intel used and still uses two. The 955 dating back to 2009 may well suffer from this. The motherboard and memory also suffer from aging, being of same age as your current Alienware.
I believe it would run the current AH quite well. Not knowing the specs of your current rig it's hard to tell whether this one would be of any improvement, though.
But: If the video card really is new, unused and under warranty and the Windows comes with the license sticker you might take this one as a starting platform for a new build. I wouldn't pay for it more than the price of the video card, though. And even a few month's usage of the VC would drop my bid significantly. If I looked right, the GeForce GTX 770 is about $330, but IIRC there are new models on the way which may cause the price to drop dramatically from that in the near future. All that considered some $300 would be the maximum I'd pay. Again, for me that price has to include only a test used video card and a legal Windows license sticker.
[edit] On second thought even the $300 starts to feel way too much. After all, as the rule of thumb for used goods the value of any item halves the moment it's carried out of the shop. Five year old components are mostly concerned as electric waste although their use value may be quite high as long as they work.
