First, let me start out by stating I have never used BitTorrent, and I know nothing about it. But from your question and the error messages you are getting, it sounds like you just need to open a port on your firewall, probably the port range the last guy just gave you.
"But" it might also mean this.
Many applications on the internet will not work behind a "PAT" configured host. PAT (Port Address Translation) allows many hosts to NAT behind one IP address. It does this by changing the TCP Port number from the standard port for the application, to some other port number. For example, if Bit Torrent used TCP port 6001, your PAT configuration would use on the back end, a TCP port number of 9333, or some other number other than 6001.
Because this occurs on the back end only, its normally not an issue. But some applications use TCP header data for session state or setup functions, and the varying port numbers can cause problems with the application, and block session setup altogether. IF thats the case, then you'll need to have a one to one NAT configuration on your router, which depending on your router, may require an additional IP address.
I realize that may sound like Greek to you, so try this.
One way to find out is to simply plug your computer directly into your cable modem or DSL connection and bypass your router. See if the application works without your router in the middle. If so, then its probably the NAT\PAT issue I described above.
Layer9
Layer9Security.com