I want a bf4 PC for $800 or less

you can start from here

i believe it will run bf4 on high setting 60+
but ultra? maybe dual GPU setup

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4440 3.1GHz Quad-Core Processor ($174.29 @ Amazon)
Motherboard: ASRock B85 Pro4 ATX LGA1150 Motherboard ($69.99 @ Newegg)
Memory: Crucial Ballistix Sport XT 8GB (2 x 4GB) DDR3-1600 Memory ($69.99 @ Newegg)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive ($49.94 @ Amazon)
Video Card: Asus GeForce GTX 770 2GB Video Card ($328.98 @ SuperBiiz)
Case: NZXT Source 220 ATX Mid Tower Case ($44.99 @ TigerDirect)
Power Supply: Corsair Builder 600W 80+ Bronze Certified ATX Power Supply ($49.99 @ Newegg)
Total: $788.17
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-11 10:48 EDT-0400)
 
PCPartPicker part list: http://pcpartpicker.com/p/385He
Price breakdown by merchant: http://pcpartpicker.com/p/385He/by_merchant/
Benchmarks: http://pcpartpicker.com/p/385He/benchmarks/

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Newegg)
Motherboard: Biostar TA970 ATX AM3+ Motherboard ($69.99 @ Newegg)
Memory: Kingston Black 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($57.99 @ NCIX US)
Video Card: Asus GeForce GTX 760 2GB Video Card ($249.99 @ NCIX US)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($44.99 @ NCIX US)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($15.99 @ Microcenter)
Operating System: Microsoft Windows 8.1 - 64-bit (OEM) (64-bit) ($97.26 @ OutletPC)
Total: $729.18


Here's a full build within your budget.