Every so often I find it amusing to find out what is the cheapest complete PC that can be built from parts on Newegg.
Today this was the result of 10 minutes of browsing.
   
APEX PC-389-C Black Steel ATX Mid Tower Computer Case
$29.99   -$10.00 Instant   $19.99
      
Seagate Barracuda ST3250312AS 250GB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
$36.99       $36.99
      
Hanns-G HW-173ABB Black 17" 5ms Widescreen LCD Monitor
$119.99   -$40.00 Instant   $79.99
      
BIOSTAR N68S AM2+/AM3 NVIDIA MCP68S Micro ATX AMD Motherboard
$49.99   -$15.00 Instant   $34.99
      
Diablotek DA Series PSDA250 250W ATX Power Supply
$10.99       $10.99
      
Pixxo KB-9AA1 Black USB Wired Standard Keyboard + Optical Mouse Combo
$19.99   -$5.00 Instant   $14.99
      
Crucial 1GB 240-Pin DDR2 SDRAM DDR2 667 (PC2 5300) Desktop Memory Model CT12864AA667
$15.99       $15.99
      
AMD Sempron 140 Sargas 2.7GHz Socket AM3 45W Single-Core Processor SDX140HBGQBOX
$37.99       $37.99
      
Patriot X-Porter 2GB Flash Drive (USB2.0 Portable) Model PSF2GUSB
$5.99       $5.99

Subtotal: $257.91
Shipped: $277.56

The flash drive is for the assumption that the person does not have any PC whatsoever, but they could go to an internet cafe or something and put a bootable Linux installer on the flash drive.

I know I didn't consider net-tops or combo deals. See if you can do better : )