A $800 budget is enough to build a pretty nice gaming computer with top notch components. The following build is a good start for him to get into PC gaming. It should play most of the modern games with ULTRA settings at 1080p without any problems.
CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($225.98 @ Newegg)
Motherboard: Asus P8Z77-V LK ATX LGA1155 Motherboard ($114.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-2133 Memory ($59.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($58.13 @ OutletPC)
Video Card: Asus GeForce GTX 760 2GB Video Card ($249.98 @ SuperBiiz)
Case: Rosewill Challenger-U3 ATX Mid Tower Case ($24.99 @ Newegg)
Power Supply: SeaSonic G 550W 80+ Gold Certified Semi-Modular ATX Power Supply ($85.99 @ Amazon)
Total: $802.05(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-06 09:58 EST-0500)