Where are you doing this (like a university?)
What ISP do you have (Comcast?)
What Bit Torrent program are you using? I'd try Transmission, it's pretty good.
It sounds like you may be being blocked, which makes a lot of sense if you are on some sort of public network like at a university where they like to block BitTorrent traffic. Also, some ISP's either throttle or (this is VERY of illegal) kill bit torrent traffic...
Can't say for sure what your problem is, though.
More or less I'd say try a bunch of different options, like try it on a different network, then with a different BT client, then from a different tracker (try BTJunkie instead of ThePirateBay, for example). If the behavior changes, that can tell you a lot about what your problem is.