The machine I just built sounds like it fits right into your budget.
I currently have it clocked @ 4Ghz and it gets to 71c max on full load :)
Case
Mother Board
Video Card
PSU
CPU i7 950 (you could save money and go with the i7 920, plenty of overclocking guides online. I wanted a challenge and potential to go higher then the 920. The 950 came with RE5 for free)
Memory
HDD
CD Rom (you may have an extra one around and won't need this.)
You could probably save some money on some things buy going with lower end. also, factor in the $100 for the DP adapter.
The total cost of my system was 2200 about. On the account that I also got an after market cooler.
Cooler Master V8
A similar build from Dell or Alienware will cost you $4,000
With CoD4 I run insane frame rates with everything maxed out. Crysis is a different story, the game engine doesn't use all of the hardware in my machine, and for that fact, I see stuttering with everything at the max, so I lower the AA to about 2x - 4x and I'm at a solid 35 - 40 fps in Eyefinity ;)
-Tanshin
P.S. Most home built systems will be better and cheaper then complete systems, that and you will know more about your system if something goes wrong. I've been building systems for 13 years or so now. If you aren't used to building your own system, I would take your time building it, and have fun! I almost enjoy building more then playing with them.