APEVIA X-TROOPER Series X-TRP-RD Black / Red Steel ATX Mid Tower Computer Case
Item #: N82E16811144266
$10.00 Mail-in Rebate
Seagate Barracuda ST1000DM003 1TB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
Item #: N82E16822148840
GIGABYTE GV-R785OC-2GD Radeon HD 7850 2GB 256-bit GDDR5 PCI Express 3.0 x16 HDCP Ready CrossFireX Support Video Card
Item #: N82E16814125419
SPARKLE R-FSP700-80ETN 700W ATX12V V2.3 / EPS12V V2.92 SLI Ready CrossFire Ready 80 PLUS PLATINUM Certified Active PFC Power ...
Item #: N82E16817103086
CORSAIR Vengeance 16GB (2 x 8GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model CMZ16GX3M2A1600C10
Item #: N82E16820233246
Intel Core i7-3770K Ivy Bridge 3.5GHz (3.9GHz Turbo) LGA 1155 77W Quad-Core Desktop Processor Intel HD Graphics 4000 BX80637I73770K
Item #: N82E16819116501
LG Black 12X Internal Blu-ray Drive 3D Playback & M-DISC Support SATA Model UH12LS29 LightScribe Support - OEM
Item #: N82E16827136246
GIGABYTE GA-Z77X-UD3H LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
Item #: N82E16813128544
$100 over your budget, but with very good components IMHO. This is assuming you have your keyboard, mouse and Operating System. If you do not, then for a decent keyboard and mouse for gaming ~$150 plus whatever for the OS of your choice. I did not put in an SSD as it does not seem like it will be of actual benefit to you. Also, prices are high for now, though Intel said they will drop soon.
This setup has plenty cooling, much better processor than anything AMD can churn out as of today, 16GB Ram plus you can upgrade to 32GB. As a side note, if you cannot make decide yourself on what you want for a system, water cooling might not be for you. Anyhow, you got plenty USB 3.0s, 1TB Harddrive with 6.0GB connection, Blu Ray drive in case you want to use it as entertainment hub. The video card has a very decent core clock speed and has the HDMI you want, which BTW can act as your audio out as well. It has overkill for powersupply and it is Platinum Certified, which will make it much more efficient.
Hope this helped. If it really needs to be under $1100, and with keyboard, mouse, etc. Let me know... I am actually looking for a few things on Newegg.com
and this was a fun side thing to do.
Note: I am making myself an entertainment hub Hackintosh Dual Booter, which casually has specs similar to this.