My setup is somewhat similar to NYRHKY94's.
It's a used AOpen Pentium 4, 1.4 GHz motherboard that I bought on ebay for $8.00.
The main reason I chose this board was for the 5 PCI slots.
I've tried and pretty much rejected the cheap USB sound cards and stick with Soundblaster cards.
It only has 512 MB or memory, and I am able to run 5 feeds with no trouble.
Two are streamed on radioreference, and the other 3 I listen to locally.
I run Debian 6.0 Linux, with NO graphical interface, no monitor and no keyboard or mouse.
I telnet into the machine from another to make changes, etc.
Scan-Denver makes a good point for recommending a dedicated machine as well.
I just checked the processes and the 3 streams I'm currently running locally combined are only using 9% CPU and 1.5% RAM resources.
Since the machine I'm using is dedicated, no other applications will be competing for CPU and RAM.
Another thing to consider is your own willingness to leave a pricey computer powered on 24 hours a day when an outdated computer will easily do the work.
Just a few things to think about.