You can cannibalize some parts from your old computer - case, power supply, hard drive, memory. If you post details of them then we could recommend compatible parts. You can also save money by using the video card on the mother board depending on the types of games you play and preferred settings.
Below is under $500. I choose these because they are good bang for the buck and mid range.
$50 Hard Drive
NeweggBusiness - Seagate Barracuda ST1000DM003 1TB 7200 RPM 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive Bare Drive
$30*2 RAM
G.SKILL Ripjaws Series 4GB (2 x 2GB) DDR3 1600 Desktop Memory Model F3-12800CL9D-4GBRL - Newegg.com
$100 Video Card
Zotac ZT-70605-10M G-SYNC support GeForce GTX 750 Ti Graphic Card - 2 GB DDR5 SDRAM - PCI Express - Newegg.com
$75 CPU
[ame="http://www.amazon.com/AMD-Athlon-Edition-3700Mhz-AD860KXBJABOX/dp/B00MU00IOQ?SubscriptionId=AKIAJTGKCKV5NXB3GYGQ&tag =siame-20&linkCode=sp1&camp=2025&creative=165953&creative ASIN=B00MU00IOQ"]Amazon.com: AMD Athlon X4 860K Black Edition CPU Quad Core FM2+ 3700Mhz 95W 4MB AD860KXBJABOX: Computers & Accessories[/ame]
~$70 Motherboard
~$50 Power Supply
~$50 Case