My goal is to build a gaming computer dedicated to Skyrim running at least high settings. My budget is about 700$ and I do not need a case, optical drive, peripherals, or OS. I'm wondering if these are compatible:
You will be fine with that Mobo. PCI-E is backwards compatible. Are you going to be overclocking? If not, drop to down to the i5 2400. Use the extra on a nicer video card. For around $100 more than the 6850, the 560 Ti resides. Which is a (spell it with me) B A U S S! (EVGA 560 Ti SuperClocked)
It will run Skyrim on Ultra @1080p no problem.
Also, what is your PSU? This monster needs a good quality 600W PSU to be safe. Anyway, if you decide against the 560 Ti, at least get a 6870. Sapphire is the way to go for AMD cards, in my opinion. SAPPHIRE Radeon HD 6870