$600-800 Gaming Computer (for BF4)

How many fps do you need to run high? This is going to be hard unless you are fine with about 30-40ish fps on high?

$800 is plenty for getting good results on maximum settings really, though obviously you'll probably want to tweak things to your satisfaction. $600 if that includes peripherals too, is more of a push.

You say you don't want to overclock, that's fine, it's not for everyone, and you don't have to to get good performance, but it does change your options a little. I have used all of the budget so there is no money for keyboard+mouse, as I'm unsure if this has to cover that too.

My first suggestion uses the FX8350 and a GTX760. A variant on the same build would be to swap to an FX8320 and upgrade the graphics card to an R9 280X, HD7970 or at a push, a GTX770.
I chose the FX8350 option because Microcenter offer them for $180 in store pickup and there is one in Houston, and because you aren't overclocking, the extra base speed will help. Having said that, if you are simply looking for the best FPS, a more expensive graphics card is likely to make more of a difference than a more expensive processor.
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-8350 4.0GHz 8-Core Processor ($192.98 @ SuperBiiz)
Motherboard: ASRock 970 PRO3 R2.0 ATX AM3+ Motherboard ($72.55 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($58.99 @ NCIX US)
Video Card: MSI GeForce GTX 760 2GB Video Card ($249.99 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($39.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Optical Drive: LG GH24NS95 DVD/CD Writer ($19.98 @ OutletPC)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($82.99 @ NCIX US)
Total: $803.45
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-23 13:52 EST-0500)


Similar, with Intel options, you have choices. As you aren't overclocking, you can skip the expensive k-series processors and Z series motherboards, so the choice is between Ivy Bridge 3*** and Haswell 4***. Haswell offers better future upgrade potential, and some new features, but in base performance it is nearly identical to its predecessor. As Ivy Bridge is cheaper, its generally better value.
Similarly to AMD, you can get an i5 4570 for $30 cheaper at your local Microcenter, which makes it better value.
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($189.99 @ Newegg)
Motherboard: ASRock H87 Pro4 ATX LGA1150 Motherboard ($80.55 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($58.99 @ NCIX US)
Video Card: MSI GeForce GTX 760 2GB Video Card ($249.99 @ Newegg)
Case: Corsair 200R ATX Mid Tower Case ($39.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Optical Drive: LG GH24NS95 DVD/CD Writer ($19.98 @ OutletPC)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($82.99 @ NCIX US)
Total: $808.46
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-23 13:57 EST-0500)

Both of those builds can be pulled under $800 by using the aforementioned Microcenter deals or by saving a bit of money here and there on motherboards (dropping to cheaper chipsets and mATX boards was an option).

If you are looking to spend nearer to $700 to give yourself money for peripherals, that is possible on both builds without sacrificing much performance, but it will mean going as cheap as possible on things like the motherboard and case.

As I've got both builds using the same graphics card, benchmark performance will be very similar. On Ultra settings, 1080P, you are looking at over 50fps average with MSAA off between 40 and 50 with 4X MSAA. As a lot of the data that exists is from the Beta still, its hard to be very specific, as I've seen some fairly different results from different sites, but they would all agree that the GTX760 is perfectly happy running BF4 at 1080P. Obviously as mentioned earlier, if you chose to spend more on graphics, they will produce incrementally better results.


EDIT - crap, I've just reread your post and as you'd stated a display resolution I assumed you already had one. Ooops.

Power Supply
Cooler Master eXtreme Power 550W ATX Power Supply $49.99

CPU
AMD FX-6300 $109.99

Motherboard
ASRock 970 Extreme3 $109.69

Memory
Corsair 8GB $74.99

Storage
Seagate 1TB 7200RPM $74.98

Video Card
Asus Radeon HD 7790 $139.99 *

Case
Fractal Design Core 3000 USB 3.0 (Black) $59.99

Optical Drive
Asus DRW-24B1ST/BLK/B/AS $16.99

Operating System
Windows 7 Home Premium SP1 (OEM) (64-bit) $82.99

Monitor
Asus VS228H-P 21.5" $147.58 *

Keyboard
Corsair Vengeance K65 Compact Mechanical Gaming Keyboard $83.99

Mouse
Corsair Vengeance M65 $54.99 *
Subtotal: $1006.16
* Mail-In Rebates: $30.00
Total: $976.16

This is how low I can go with everything..Either raise the budget by 100 more,because with a good/decent gpu it costs more than 200 and with the gpu i recommended you will only get to medium setting in good fps.

High fps will be horrible unless the budget is up,the gpu takes up a lot of money and with the monitor,keyboard,mouse and os taking up the money,Bf4 will stay at medium settings! This is a good build though for that decent much of money!!

If you are not inclusing the keyboard,mouse and monitor with his budget,I will recommend this!

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
Motherboard: ASRock 970 Extreme3 ATX AM3+ Motherboard ($109.69 @ NCIX US)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($74.98 @ SuperBiiz)
Video Card: EVGA GeForce GTX 770 2GB Video Card ($339.99 @ NCIX US)
Case: Fractal Design Core 3000 USB 3.0 (Black) ATX Mid Tower Case ($59.99 @ NCIX US)
Power Supply: Cooler Master eXtreme Power 550W ATX Power Supply ($49.99 @ Mwave)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($82.99 @ NCIX US)
Total: $919.60
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-23 14:34 EST-0500)

Or the budget:

PCPartPicker part list: http://pcpartpicker.com/p/27axg
Price breakdown by merchant: http://pcpartpicker.com/p/27axg/by_merchant/
Benchmarks: http://pcpartpicker.com/p/27axg/benchmarks/

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
Motherboard: ASRock 970 Extreme3 ATX AM3+ Motherboard ($109.69 @ NCIX US)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($74.98 @ SuperBiiz)
Video Card: EVGA GeForce GTX 660 2GB Video Card ($214.99 @ Amazon)
Case: Fractal Design Core 3000 USB 3.0 (Black) ATX Mid Tower Case ($59.99 @ NCIX US)
Power Supply: Cooler Master eXtreme Power 550W ATX Power Supply ($49.99 @ Mwave)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($82.99 @ NCIX US)
Total: $794.60
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-23 14:36 EST-0500)