400$ Gaming PC Build

So -
CPU: AMD Athlon X4 760K 3.8GHz Quad-Core Processor ($73.98 @ OutletPC)
Motherboard: ASRock FM2A75M Pro4+ Micro ATX FM2+ Motherboard
Memory: G.Skill Value 4GB (1 x 4GB) DDR3-1600 Memory ($37.98 @ OutletPC)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($48.25 @ Newegg)
Video Card: MSI Radeon R7 265 2GB Video Card ($134.99 @ Amazon)
Case: Rosewill FBM-01 MicroATX Mini Tower Case ($29.99 @ Amazon)
Power Supply: EVGA 430W 80+ Certified ATX Power Supply ($19.99 @ Micro Center)
Total: $345.18

Try 2 x 2gb ram - runs faster than 1 x 4gb

Your mini mobo will fit your mini case.
 
Try -
CPU: AMD A10-7850K 3.7GHz Quad-Core Processor ($148.98 @ OutletPC)
Motherboard: Asus A88X-PRO ATX FM2+ Motherboard ($99.49 @ Newegg)
Memory: Mushkin Redline 8GB (2 x 4GB) DDR3-2400 Memory ($79.99 @ Newegg)
Storage: Seagate Barracuda 250GB 3.5" 7200RPM Internal Hard Drive ($44.49 @ Amazon)
Case: NZXT Source 210 (White) ATX Mid Tower Case ($34.99 @ Directron)
Power Supply: SeaSonic 300W 80+ Bronze Certified ATX Power Supply ($42.98 @ Newegg)
Total: $450.92
 

Also runs at lower speeds which means it will perform worse, but okay.

Caviar Green: Twice storage, more energy efficient and will perform worse.
Toshiba: Half the storage and will perform better.

You can pick OP.