Yeah, any very basic distro might be alright like that if you do not install X and give it some good swap space. Just setup samba to share the MP3's out to other computers.
DamnSmallLinux would be easy to install. It's got X and fluxbox and a light web browser, it is a very basic debian otherwise and installs like knoppix.
You would need to boot using cheatcodes to run in text mode the first time, then probably run cfdisk and create a swap partition on your hard drive.
With that done, you should be able to reboot normally into fluxbox (if your video hardware is half-way decent) and install from there (it will automatically see and use the swap partition).