I am connected to the Internet through a router that I forgot the password to. So I can't open up ports like usual. How can I scan for open ports that I can use for bittorrent? I would like to use a program in the Linux terminal to scan for usable ports. Can I use a well-known port?
Chances are all your ports are open going out, but that is not the information you need, and you cannot get that internally. You need an external port scan (Google port scan).
One that I always have used is "Shields up"
http://www.grc.com/x/ne.dll?rh1dkyd2 (click proceed, then click "User Specified Custom Port Probe" and read the directions)
You can also go here:
http://www.t1shopper.com/tools/port-scan/ (enter ports 1025-65535 and click scan)
In the long run, you might just be better off setting the router back to factory defaults and putting in a password you remember.
Also bear in mind that even if there are Static NATS in place each NAT has to assign a static external port and a static internal IP, so even if you find an open port there's no guarantee that it forwards to your computer anymore unless it's kept it's IP address since you last used bittorrent.