[Nyx]

You can build a entry-level gaming PC for 700 $...
Just check AMD Athlon and phenoms...
and cheap Nvidia cards (Gt 630, etc.)

Oh god, please don't ever suggest a GT 630 ever. That is way behind man, probably would have issues running Minecraft with that shit.

Anyways:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Newegg)
Motherboard: Gigabyte GA-78LMT-USB3 Micro ATX AM3+ Motherboard ($59.99 @ Amazon)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR3-1600 Memory ($66.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($63.54 @ Amazon)
Video Card: MSI Radeon R9 270X 2GB Video Card ($229.99 @ Amazon)
Case: Rosewill FBM-01 MicroATX Mini Tower Case ($22.97 @ Amazon)
Power Supply: EVGA 500W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($44.99 @ Newegg)
Total: $600.46
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-12 07:43 EST-0500)
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Could even upgrade if you wanted since there is more spending room. This could probably play BF4 at High settings, probably not Ultra though.