If you're handy, I'd suggest getting a first-gen ATV. You can install OS X Tiger on it, then you're left with a semi-functioning computer with a 1GHz Celeron M and 256mb of RAM. Core Image and audio don't work though (though you can use an external DAC). Then you can use it for torrents, jDownloader, samba shares etc. You could leave it headless and use VNC to queue up a torrent.
You just need a TV with HDMI or component inputs to set it up, after that you can remove the monitor and control it from another machine. I understand that that might not be an ideal solution, just shedding some light on it.
eBay, Craigslist (if you're near a major city), or keep an eye on the iBook deals page on Low End Mac (which is only updated a few times a year).
$150 is the more common price, so you'll have to be vigilant to find one for $100.
You could consider an iBook G3, which is far cheaper, but they do not have USB 2.0. Although you could connect a Firewire 400 external hard drive to them.