What do you think of some of these components?
$125 +fs Intel Core i3-2120 Sandy Bridge (hyper-threading dual-core 3.3 GHz) LGA1155 CPU
or $205 +fs Intel Core i5-2500K Sandy Bridge (quad-core 3.3 GHz unlocked) LGA1155 CPU
optional $35 +fs CoolerMaster Hyper 212 Evo cooler
$110 +7½sh ASRock Z77 Pro4-M micro-ATX LGA1155 motherboard
or $150 +7½sh Asus P8Z77-V LK ATX LGA1155 motherboard
$50 -10 combo +fs 2x4 GiB PC3-12800 Corsair Vengeance CMZ8GX3M2A1600C9B (DDR3-1600, CAS 9, 1.5 V) memory
or $55 -10 combo +fs 2x4 GiB PC3-12800 Corsair Vengeance CMZ8GX3M2A1600C9G (DDR3-1600, CAS 9, 1.35 V) memory
$200 +fs Sapphire Radeon HD6950 2GB 11188-22-20G graphics card
or $240 +fs XFX Radeon HD7850 2GB FX-785A-CNFC graphics card
or $205 +7½sh ECS GeForce GTX560Ti 1GB NGTX560TI-1GPI-F1 graphics card
$0 Integrated Realtek ALC892 audio
optional $110 +fs 128 GB Samsung 830 SSD
$75 -17 combo +fs ½ TB Western Digital WD5000AAKX Caviar Blue hard-drive
or $110 -18 combo +fs 1 TB Samsung HD103SJ SpinPoint F3 hard-drive
$17 +fs Samsung SH-222BB DVD-RW
or $58 -8 code "EMCNEJE49" +fs Asus BC-12B1ST BD-ROM/DVD-RW
$65 +fs -10MIR Antec Three Hundred Illusion ATX mid-tower case
or $55 +3sh Antec Three Hundred ATX mid-tower case
$45 +fs Antec EarthWatts Green EA-430 (32 A @ +12 V) power supply
or $55 +fs Antec BP550 Plus (37 A @ +12 V) power supply
or $60 +9½sh SeaSonic M12II 520 Bronze (40 A @ +12 V) modular power supply
or $43 +8sh Cheap ATX case and PSU (30 A @ +12 V)
$100 +fs Microsoft Windows 7 Home Premium 64-bit OEM
$8 +4sh Microsoft Keyboard 200
$16 +fs Microsoft Comfort Mouse 4500 (with 5 buttons)
or $55 +fs Microsoft Wireless Desktop 3000 keyboard and 5-button mouse
$25 +fs Logitech S220 2.1-channel speakers
or $46 +fs or $40 +fs Logitech Z313 2.1-channel speakers
$180 +fs ViewSonic VX2336S-LED 23" 1920x1080 e-IPS LCD monitor
or $120 -12 code "EMCNEJB45" +fs Acer G215HVAbd 21½" 1920x1080 TN LCD monitor
or $140 -14 code "EMCNEJB46" +fs Acer G235HAbd 23" 1920x1080 TN LCD monitor
or $225 +fs Dell UltraSharp U2212HM 21½" 1920x1080 e-IPS LCD monitor
or $270 -30 code "EMCNEJE228" +fs Hanns-G HZ281HPB 27½'' 1920x1200 TN LCD monitor
or $250 +9sh Dell UltraSharp U2312HM 23" 1920x1080 e-IPS LCD monitor
or $189 +tax +fs Refurbished Dell UltraSharp U2312HM 23" 1920x1080 e-IPS LCD monitor
90-day warrantyor $310 +fs Dell UltraSharp U2412M 24" 1920x1200 e-IPS LCD monitor
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$989 +10½ shipping -10 MIR
That's pretty close to your $1000 budget.