Actually your router *is* a computer. It typically uses Linux. It's just a computer dedicated to a single task, routing. Because it is a computer, it’s possible to take advantage of that fact and have it do more. For example, you can install third-party firmware (dd-wrt, tomato, openwrt, etc.) to some routers and using optional software, install and configure the necessary apps (in your case, Linux has a program called Transmission for handling torrents). There are even a few routers that support torrents w/ their stock firmware.
In the case of a combo modem+router, it gets a bit trickier since most of these third-party firmware solutions don’t incorporate modem support. They’re intended solely to provide routing functions. But if you’re goal is simply to have torrent support without a dedicated PC/laptop, nothing prevents you from getting a dd-wrt/tomato/openwrt compatible router, disabling its routing features, installing Transmission (just to use that as an example), and patching it to your existing router. IOW, create your own mini-computer. I’d done something similar w/ an ASUS WL-520GU. I’ve turned it into a media player (using Linux MPD), which is then wirelessly bridged to my primary router ( http://www.youtube.com/watch?v=Bp26xFBwrJs ). Works great. Of course, I could have wired it to my primary router instead, but I wanted it connected to my home stereo, so wireless bridging was more practical.
So yeah, assuming you can’t find a commercial modem+router w/ torrent support, in a sort of way, you can create for yourself a mini-computer for such dedicated tasks. Again, the only complication in your case is the fact you’re trying to do it w/a combo modem+router, which throws a monkey wrench into the process. But if you could live w/ the addition of one small box (router) and third-party firmware, and feel up to the challenge of doing the work yourself, it’s at least possible. There are already guides on the net for adding Transmission to these routers, so it’s not as if you have to figure it all out yourself.