Can i build a pc for 400 or less for arkham knight

Solution
This should be good:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD A10-7700K 3.4GHz Quad-Core Processor ($129.99 @ Amazon)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($73.77 @ Amazon)
Memory: G.Skill Ripjaws X Series 4GB (2 x 2GB) DDR3-1866 Memory ($45.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.99 @ Amazon)
Case: Cooler Master N200 MicroATX Mid Tower Case ($44.99 @ Newegg)
Power Supply: SeaSonic S12II 380W 80+ Bronze Certified ATX Power Supply ($55.98 @ Newegg)
Total: $405.71
Prices include shipping, taxes, and discounts when...
right now if he dont care about use a beta software windows 10 is free.
if he in school see if his school part of the microsoft edu it may be able to get widnows for a discounted price.
to the op your best bet is to build a 400.00 base pc that let you drop in a higher end video card and cpu when the funds let you.
 
This should be good:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD A10-7700K 3.4GHz Quad-Core Processor ($129.99 @ Amazon)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($73.77 @ Amazon)
Memory: G.Skill Ripjaws X Series 4GB (2 x 2GB) DDR3-1866 Memory ($45.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.99 @ Amazon)
Case: Cooler Master N200 MicroATX Mid Tower Case ($44.99 @ Newegg)
Power Supply: SeaSonic S12II 380W 80+ Bronze Certified ATX Power Supply ($55.98 @ Newegg)
Total: $405.71
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-02-11 15:37 EST-0500
 
Solution
PCPartPicker part list: http://pcpartpicker.com/p/hZvmJx
Price breakdown by merchant: http://pcpartpicker.com/p/hZvmJx/by_merchant/

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($49.99 @ Micro Center)
Motherboard: Asus H97M-E/CSM Micro ATX LGA1150 Motherboard ($84.99 @ SuperBiiz)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($43.79 @ OutletPC)
Power Supply: EVGA 750W 80+ Bronze Certified Semi-Modular ATX Power Supply ($54.99 @ Newegg)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($12.99 @ SuperBiiz)
Total: $306.74
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-02-11 15:39 EST-0500
used the h97 to let you drop in a brodwell cpu later on. also used the 750w unit so you can put any gpu in. the evga 600b are about 10.00 cheaper righrt now when there onsale there 20.00 less then the 750 unit.