Not doable for $600
This would for $695 if you heavily OC the CPU
G.SKILL Value Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1333
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231422
AMD Phenom II X4 970 Deneb 3.5GHz Socket AM3 125W Quad-Core Desktop Processor
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103893
COOLER MASTER Hyper 212 EVO RR-212E-20PK-R2 Continuous Direct Contact 120mm Sleeve CPU Cooler
http://www.newegg.com/Product/Product.aspx?Item=N82E16835103099
SAMSUNG 22X DVD Burner
http://www.newegg.com/Product/Product.aspx?Item=N82E16827151244
BitFenix Merc Beta Black Steel / Plastic ATX Mid Tower Computer Case
http://www.newegg.com/Product/Product.aspx?Item=N82E16811345015
Western Digital Caviar Blue WD5000AAKX 500GB 7200 RPM 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136769
GIGABYTE GA-970A-DS3 AM3+ AMD 970 SATA 6Gb/s USB 3.0 ATX AMD Motherboard
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128553
EVGA 015-P3-1480-KR GeForce GTX 480 (Fermi) 1536MB 384-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130759
CORSAIR Enthusiast Series TX650 V2 650W ATX12V v2.31/ EPS12V v2.92 80 PLUS BRONZE Certified Active PFC High Performance Power Supply
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139020
$695
Now that does not include windows so theres more expense if you dont have it already. The GPU is an old model famous for sucking power and running hot but it will do what you want and is the most grunt we can get and still try to fit your budget. You can save cash if you have an old SATA HDD or DVD drive lying around and recycle them.