While I am not a fan of pre-built boxes you could also check the HP site.
Buy HP Laptops, Notebook PCs, Printers, Digital Cameras, Desktop Computers, Televisions, Handhelds, Scanners, Monitors, Projectors, and Calculators direct from the HP Home & Home Office Store
A quick run through their site pulled up the following after a bit of customizing:
HP Pavilion Elite d5000z ATX series
Operating system Genuine Windows Vista Home Premium with Service Pack 1 (64-bit)
Processor AMD Phenom(TM) 9550 quad-core processor (2.2GHz)
Memory 4GB DDR2-800MHz dual channel SDRAM (4x1024)
Graphics Card 512MB NVIDIA GeForce 9500GS, DVI-I, VGA, HDMI
Hard Drive 500GB 7200 rpm SATA 3Gb/s hard drive
Primary CD/DVD Drive LightScribe 16X max. DVD+/-R/RW SuperMulti drive
Front Productivity Ports 15-in-1 memory card reader, 2 USB, 1394, audio
Sound Card Integrated 7.1 channel sound w/front audio ports
Security Software Norton Internet Security(TM) 2008 - 15 month
Productivity Software Microsoft(R) Works 9.0
Speakers HP stereo speakers with subwoofer and remote (2.1)
Keyboard and Mouse HP keyboard and HP optical mouse
Monitor HP w1907 19" LCD Wide Flat Panel Monitor
Total: $1,229.99
Free shipping but not including tax
Fairly close to your target price and will outperform the PC based on the specs you listed initially by a good bit.