2k budget... gamer... oooh. Big things can be done.
First of all, you need to MASSIVELY upgrade your monitor expectations. A couple of piddly 23 inchers? HARDLY. You should go for a massive 30" screen for gaming + a secondary screen for non-gaming, or a big-ass 3-screen 5760x1080 eyefinity setup.
Option A ($850): go to e-bay and look for a "pixel perfect" Yamasaki Leonidas (not one of the crossovers - you need one of the Korean versions that have only a single DVI input and no OSD). Note these monitors will not be covered by warranty, so there is some risk.
Then if you need a second monitor, add a Asus VS229H-P:
http://www.buy.com/prod/asus-vs229h-p-21-5-led-backit-lcd-monitor-50-000-000-1-14ms-1920x1080/224928560.html?listingId=-1
(ok, in retrospect, a 27" 2560x1440 monitor - again sticking to the limitation on only one type of input & no OSD - might be more reasonable)
Option B ($705): get 3 Dell u2312hm. Among the best of the gaming monitors, the IPS will keep them from looking funky in the long eyefinity setup.
http://www.provantage.com/dell-469-1253~7DELL22K.htm?source=googleps
I'll assume you go with Option B for budgeting the rest of the suggestions.
Core Components: $446
i5-3570k - $216
MSI Z77A-GD65 - $165
CoolerMaster 212 Evo - $28
Team 2x4gb 1600mhz - $37
Warning: Spoiler! (Click to show)
Supporting Components: $338
Bit Fenix Raider - $70 (on special, price may not last)
XFX Core 750w - $85-$25 rebate (another great deal on a high quality supply that, yes, has enough juice for tri-fire)
Plextor 128gb m5S SSD - $100 (sale on a top brand)
Hitachi 1TB HDD - $70
DVD-burner - $13
Warning: Spoiler! (Click to show)
Video Cards: $600 - $40 rebate (and you get Sleeping Dogs for free... yay?)
2x Sapphire Radeon 7950 (good cooler, too)
http://us.ncix.com/products/?sku=65970&vpn=BFC%2DRDR%2D300%2DKKN1%2DRP&manufacture=BitFenix&promoid=1373
Tower + screens total = $2024 AMIR, ($2089 before rebates)
(Not including windows, peripherals. Does include shipping.)
You could go under the $2000 mark if you didn't get a motherboard & PSU capable of adding a third 7950 (basically replace the motherboard above with a Gigabyte z77x-ud3h), but I thought you might want the upgrade capacity. Or if you waited on SSD you could get under 2k. Or if you went for a cheaper case like the Bit Fenix Outlaw (-$35).
All in all you go from the moderate, capable gaming system in your OP (probably cheaper as well...) to a monster triple-monitor Crossfire marvel for 2k.
When comparing with other builds in this thread, don't forget I'm budgeting for a 3x Dell u2312hm eyefinity setup within the 2k suggested. Ok, nearly within the 2k budget limit.
Edited by MisterFred - 9/18/12 at 9:59pm