Antec Sonnata III Case - $105 @ mwave + shipping
MB - ASUS M2N-VM
http://www.mwave.com/mwave/viewspec.hmx?scriteria=BA24564 - $59 @ mwave
CPU - AMD 4600 dual core - Brisbane - $56 @ mwave
RAM - Kingston 800 DDR2 2x1gb sticks - $39.50 @ mwave
Hard Disk - assuming you'll just use this for boot/programs and use the external drive for music storage. Though, this MB and case will support multiple hard drives in RAID 0, 1, or 5 - Western Digital SATA2 - 250gb drive -
http://www.mwave.com/mwave/Skusearch.hmx?scriteria=AA36090 - $52 $ mwave
Wireless - Linksys PCI network card with antenna -
http://www.mwave.com/mwave/viewspec.hmx?scriteria=AA69060 - $16 @ mwave
You'll have to add in shipping but that shouldnt be too much depending on where you are.
I'm assuming you have an OS already. Also, if you pay an extra $10, they'll mount the CPU and heat sink, mount the RAM, and test it all out prior to shipping. You'll still have to put it all in the case, wire the drive, etc. but it's a nice little system for not a lot of money. The Sonata case is nice and quiet - much quieter than a Dell laptop or a Shuttle.
Obviously, you can do a different MB or CPU if you wish. I was just laying out known good pieces that are value priced. The wireless - you can use a USB to external wifi if you prefer. The card just saves desktop space, cable clutter, etc.
Bryan