I just did some modifications to the build you provided, that jsut lowered the price into your budget.
PCPartPicker part list:
http://pcpartpicker.com/p/2snP9
Price breakdown by merchant: http://pcpartpicker.com/p/2snP9/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2snP9/benchmarks/
CPU: AMD A10-5800K 3.8GHz Quad-Core Processor ($89.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.99 @ Microcenter)
Motherboard: Asus F2A55-M/CSM Micro ATX FM2 Motherboard ($75.99 @ Mwave)
Memory: A-Data XPG Gaming Series 4GB (1 x 4GB) DDR3-1600 Memory ($39.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ NCIX US)
Video Card: MSI GeForce GTX 650 Ti 1GB Video Card ($148.98 @ SuperBiiz)
Case: Corsair 200R ATX Mid Tower Case ($54.99 @ NCIX US)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($44.61 @ B&H)
Total: $544.53
The main difference is just the cooler and the case.