My apologies, I didnt realize this was a Laptop. Have you tried removing the battery and having it powered using the charger, if yes does the problem still persist?
From my personal experience, I was able to setup a solid room shaking 5.2 sound system with $700. I did however buy stuff second hand from ebay and local listings. But with your constraints. I would suggest a sound system in a box. Forgot to mention take a look at Paradigm since you have a...
It is most certainly your Dual core processor, you should surely invest in at least a Quad core CPU. One other thing you can do is update your graphic drivers.
Is your GPU Driver up to date? I know CSGO recently had a big update with its UI, and some people noticed frame drops. Also what are your in game video setting at?
With that kind of cpu cooler ur temps shouldnt go to 80C, maybe the cpu cooler is not touching the cpu properly.
Edit: unless you've overclocked it to the max.
If you are not going to overclock at all, don't bother getting the unlocked version as it will save a few bucks. As for the cpu cooler, the stock Intel cooler will be plenty for the i7 6700. These new processors are very efficient, and don't produce a lot of heat.