Verified answer

This system should be able to play bf3 quite well, I just slapped it together really quick, it came out to $809.20, but i built it with some recommended upgrades, although you do not need them all, such as you don't need the Hard drive, which is an extra $216 if you plan to use your old one, you wont have that expense, I also added a blu-ray writer, which you may not want, or want something different. I also included windows 7, a case, and a power supply, (you need at least a decent 550 watt or higher supply) which you may or may not need, and a water cooler for the cpu. I chose a decent inexpensive gigabyte motherboard for a socket am3+ amd processor to save a few bucks and configured it with a decent, yet inexpensive quad-core amd cpu. Set it up with the almost the same video card as you chose, but although your choice will play bf3 well, there is room for improvement once you cut some costs elsewhere. Note: if you go with a different board, make sure it does NOT have onboard video. It causes problems when using your computer for gaming. I also chose AMD over intel for your cpu as AMD CPUs usually provide similar performance and reliability for lower costs. The system I built for you, you can easily edit to exactly what you want, or build a new one from scratch. Once you are done building it, it will be easy to show off to your parents as a well thought out build plan and by the way, you can use a lot of your old parts for it if they are compatable including cabling, most motherboards, power supplies, and video cards come with adequate cabling already to get the job done, just make sure they are included before purchasing them. if not, cabling is cheap to buy. Also, a lot of CPUs and cpu coolers come with thermal compound too which you will need. PCPartspicker also has a cool feature for adding custom parts, which is useful for using a part that they don't show, Also check out pricewatch for other options while building.

I'd design you one, but I'm lazy. Check Newegg.com. They nearly always have combo deals that can save you like $100.

http://www.newegg.com/DIY-PC-Combos/PromotionStore...

And these "supercombos" will range in price, making it easy to find one in your price range.

For example:

http://www.newegg.com/Product/ComboBundleDetails.a...

Also, why 4 RAM slots? There's no real benefit to having more than two unless you hope to add more RAM in the future without taking out your current sticks.