I believe by "barring OS & screen" the OP meant without OS and screen - in which case I would suggest this: Overclock the processor & it'll handle 1080p games fine.
PCPartPicker part list:
http://pcpartpicker.com/p/pH9yQ7
Price breakdown by merchant: http://pcpartpicker.com/p/pH9yQ7/by_merchant/
CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.99 @ NCIX US)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($48.99 @ Mwave)
Memory: Crucial 8GB (1 x 8GB) DDR3-1600 Memory ($66.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: Asus Radeon R9 270 2GB DirectCU II Video Card ($129.99 @ Newegg)
Case: Silverstone PS08B (Black) MicroATX Mid Tower Case ($29.99 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Newegg)
Total: $410.93
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-11-11 11:52 EST-0500