I'd want to run games like COD4 in 1080i, I've got my own Full HD monitor so I won't be needing that. My budget is really up to £500 but if it's any cheaper then that'd be better because I don't actually have the money at the moment. Basically, I'd just like a list of every part I need if I'm completely building it from scrach, and want them to be compatible with each other because I don't want to buy anything that won't work. Reply to person below: No, I get paid at the end of the month so I'll have the money then and I want to build my own computer, just need some guidance.
-AMD Phenom II X4 840
-6 GB cheap DDR3 RAM
-any tower case
-6950 or 6890 (first one is better=more expensive)
-AM3+ motherboard (any will do, just check that it has 1 x16 PCI-E slot and at least 4 places for RAM adn correct SATA for HDD)
-HDD of your needs
All in all 500$-650$
Processor: Intel Core i3-2120 3.3GHz Socket 1155 Dual-Core Processor (£109.61)
Motherboard: ASrock Z68 PRO3 Socket 1155 ATX Motherboard (£99.09)
Memory: Kingston 4GB (2 x 2GB) DDR3 1600MHz HyperX Memory Kit (£32.81)
Note: This memory IS on the motherboard's QVL (qualified vendors list), so it's guaranteed to work
Video card: Asus GTX 560 DirectCU 1GB GDDR5 Graphics Card (£149.99)
Power supply: Cooler Master GX 750W 80 Plus Certified PSU (£68.42)
Case: Antec Three Hundred Mid-Tower ATX Case (£48.99)
I've built two machines with this case, and it's very nice to work in, quite roomy. Add a 120mm fan to the side panel for even better cooling.
Hard disk: Western Digital 500GB Caviar Blue SATA 6Gbps 7200rpm 3.5" Hard Drive (£31.06)
Optical drive: Sony Optiarc AD-52605 SATA DVD Burner (£14.99)
Keyboard: Logitech Deluxe 250 Black USB Wired Keyboard (£6.09)
Mouse: Microsoft Optical Mouse 200 for Business USB Wired Mouse (£6.33)
SYSTEM TOTAL (including VAT): £567.38
Just slightly over your budget, but not by much. eBuyer.com has free "within 5 working days" shipping, too.
With this motherboard/processor/graphics card combination, you should be able to play the games you mentioned at 1920x1080 at high settings at least, if not max settings, and get a very nice frame rate.
Hope that helped!
UPDATE: I assumed that you would have your own copy of Windows 7, but in case you don't, you can get the OEM version of Windows 7 Home Premium 64-bit from eBuyer.com for £68.75. See link in Source(s) below.
Good luck! Enjoy your new PC!