400$ gaming pc

Solution
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($116.99 @ Amazon)
Motherboard: ASRock H97M Micro ATX LGA1150 Motherboard ($75.66 @ Newegg)
Memory: A-Data XPG V1.0 4GB (1 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Video Card: Gigabyte Radeon R7 260X 2GB Video Card ($109.99 @ Newegg)
Case: Thermaltake VL80001W2Z ATX Mid Tower Case ($22.99 @ Micro Center)
Power Supply: XFX TS 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($13.99 @ Newegg)
Total: $405.60
Prices include shipping...
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($116.99 @ Amazon)
Motherboard: ASRock H97M Micro ATX LGA1150 Motherboard ($75.66 @ Newegg)
Memory: A-Data XPG V1.0 4GB (1 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Video Card: Gigabyte Radeon R7 260X 2GB Video Card ($109.99 @ Newegg)
Case: Thermaltake VL80001W2Z ATX Mid Tower Case ($22.99 @ Micro Center)
Power Supply: XFX TS 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($13.99 @ Newegg)
Total: $405.60
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-28 10:31 EDT-0400
 
Solution
The H81 platform works with Haswell, however be sure to do a BIOS upgrade for good measure. You will be missing USB 3.0 with this setup if that matters. The swap to an H81 board instead of an H87/H97 board (like Eduello proposed) allows you to get into a 270x GPU...

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4150 3.5GHz Dual-Core Processor ($116.99 @ Amazon)
Motherboard: Gigabyte GA-H81M-DS2V Micro ATX LGA1150 Motherboard ($54.99 @ Newegg)
Memory: G.Skill Ripjaws Series 4GB (2 x 2GB) DDR3-1600 Memory ($43.20 @ Newegg)
Video Card: XFX Radeon R9 270X 2GB Double Dissipation Video Card ($159.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Optical Drive: Samsung SH-224DB/RSBS DVD/CD Writer ($14.99 @ Newegg)
Total: $416.15
 


Why do you have 4gbs of RAM in 2x 2gb sticks? It's cheaper to go with a single stick of 4gb. But besides that I would go with this build. You will get better performance with a better GPU than you would by having a new MOBO.
 


A single module will have the memory in single channel mode which is less than ideal. Installing the memory in pair will take advantage of the dual memory controllers. Yes a single module is cheaper, but not by a dollar or two (keeping the same latency). Yes the percentage performance loss running in single channel mode is in the single digits, but there is not need for it...
 


With a $400 budget the OP will have to make some decisions around that as well as the potential need for USB 3.0. Concessions will need to be made either way, but IMHO that should never include loosing performance for a potential upgrade memory down the road. For all we know 4GB is all the OP would ever need, and DDR3 prices may drop through the floor when DDR4 becomes more mainstream.