same has happend to me many times, what i did was defrag my pc and run countless anti virus stuff. after that it worked. i could run chrome fine along with my games.
personally i would say dont use and alienware at all, first one i ever got did the same thing in 3 days. when i called they said nope cant give a refund back cause some crap. if possible go pc or a laptop, just not alienware.
for graphics i would recommend this, http://www.amd.com/en-us/products/graphics/desktop/6000/6450
its not on my gaming pc but on my personal one, it can run skyrim ultra not bad at all. also i would suggest newegg.com for shopping. great prices and deals.