Amazon.com: Intel Core i7-3930K Hexa-Core Processor 3.2 Ghz 12 MB Cache LGA 2011 - BX80619I73930K: Electronics
Amazon.com: ASUS P9X79 LGA 2011 Intel X79 SATA 6Gb/s USB 3.0 ATX Intel Motherboard: Computers & Accessories
Amazon.com: Kingston Technology HyperX 16 GB Kit (4x4 GB Modules) 16 Quad Channel Kit 1600 (PC3 12800) 240-Pin DDR3 SDRAM KHX1600C9D3K4/16GX: Electronics
Amazon.com: Samsung Electronics 840 Pro Series 2.5-Inch 256 GB SATA 6GB/s Solid State Drive MZ-7PD256BW: Computers & Accessories
Amazon.com: Corsair Carbide Series Black 300R Windowed Computer Case (CC-9011017-WW): Computers & Accessories
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Amazon.com: EVGA GeForce GTX670 FTW 2048MB GDDR5 256bit, Dual Dual-Link DVI, HDMI, DisplayPort, 4-Way SLI Ready Graphics Card Graphics Cards 02G-P4-2678-KR: Electronics
Amazon.com: Corsair Enthusiast Series 650-Watt 80 Plus Bronze Certified Power Supply Compatible with Core i3, i5, i7 and platforms - TX650: Electronics
Amazon.com: Seagate ST2000DM001 Barracuda 7200RPM 2 TB SATA 6 GB/s NCQ 64 MB Cache 3.5-Inch Internal Bare Drive: Electronics
Amazon.com: Cooler Master Hyper 212 EVO - CPU Cooler with 120mm PWM Fan (RR-212E-20PK-R2): Electronics
Amazon.com: Windows 7 Home Premium SP1 64bit (Full) System Builder DVD 1 Pack: Software
Ended up being $1980.81 for me, so it should be perfect for your budget. Obviously, storage will be up to you so if you need more storage, feel free to go with a 3TB drive or go with a couple drives if you want. Seagate's Barracuda drives are pretty good and Western Digital's Caviar Black drives are great as well.
Overall, this machine will be an absolute beast of a video editing system and it'll be a beast of a gamer as well. If you want better gaming performance, feel free to drop in two of those GTX 670's or just upgrade to a GTX 680.
Hope it helps.