Note: an extremely long post, but hopefully you can find your answer in the first few lines. If not, the rest is background info that might help
I do not really understand your setup.
Is it like this?
wall socket - cablemodem - router - PC
In that case you need to enable port forwarding in your router (the Linksys one). In the manual that came with the router (you can google for one if you don't have it anymore) you should be able to find how to access the router configuration. Usually it's a simple webpage where you can configure all sorts of stuff including port forwarding. Just be sure to forward the same ports on the router as uTorrent uses for its incoming connections.
(you can check and/or configure the port within uTorrent via Options->Preferences->Connections)
You will need to tell the router to send all traffic on port X (whatever is configured in uTorrent) to the local address of your PC. The local address is usually 192.168.y.z. (y and z can be anywhere from 0 to 254), but this can be determined by the following command on your PC:
Start -> run
cmd
press enter
ipconfig
press enter
(look for the entry "IP address")
Hope this helps!
p.s. port forwarding is not related to having dynamic or static IP addresses, but rather because you have a router, read on below for the explanation.
a little background info:
All programs communicating across the internet use ip adresses to determine the physical internet connection to connect to. Ports are used so different programs can communicate with the same machine simultaneously. So the full address from one application to another (say webbrowser, to webserver or one MSN client to another MSN client) is actually ip address + port: 123.123.123.123:12345
This says: I want to connect to application 12345 at machine 123.123.123.123.
Websurfing uses port 80 (usually) so when you request a website,
www.tfproject.org, your browser translates that to
www.tfproject.org:80
(try it, you can specify the port number in your browser using the : (colon) like I just did. 80 will ususally give the same result as not specifying the port number, but 81 will not work)
Bittorrent works the same way. Every client tells the tracker what Port(s) the bittorrent software is using. That's why the clients can connect to each other; they get the ip address and port number from the tracker.
What a router does is hide multiple machines (up to 4 with your router) behind a single IP adress. When a local machine (a pc behind the router) communicates from behind the router to the Internet (for example: web surfing) the router remembers which of the 4 pc's the request came from. It then can then send the answer from the website back to that machine. However, when a connection comes from the internet without a request by a local PC, the router doesn't know which PC to send it to. That's were port forwarding comes in.
By telling the router that all traffic that comes in at port 10000 is meant for PC1, the router will pass that right through to PC1. That's how one single IP address can be used by multiple machines simultaneously: the router uses the ports to determine which machine the data is meant for.
Because of the way that the Internet works, a combination between ip address and port number is unique for a single application. Only one application can use port 4000 for example. That's why uTorrent allows you to specify the port. This allows you to specify port 5000 for PC1, 5001 for PC2, and so on and so on.
What uTorrent does is open port X on the PC for incoming connections (and tells the tracker that port X is available). However uTorrent has no knowledge or control over the router. That's why you need to tell the router yourself.
Static or dynamic IP address
For this situation dynamic or static IP adressing makes no difference.
Your uTorrent application tells the tracker: I'm available at the same IP address I'm calling from, and I'm using port 5678
This means that the tracker, seeing an incoming connection from ip address 123.123.123.123 records that client as available at port 5678.
Now, uTorrent repeats this announcement every 30 minutes or so. So if your IP adress changes, the tracker will know very quickly and tell it to the other clients.
Usually your IP address changes only if your Internet connection gets disconnected. But it can happen during a live connection, and then you'll have problems with incoming connections for a little while. This will fix itself and should not be a real problem.
How to change from dynamic to static IP address?
Only your ISP will determine which IP address your connection will get. Some ISPs use static addressing where you get a permanent fixed IP address, but most often they'll use something called DHCP (Dynamic Host Configuration Protocol).
With DHCP, your cable modem requests an IP address every so often. The DHCP server of your ISP then assigns an IP address.
If you upgrade your subscription, the meganism will remain the same but the DHCP server will be configured to give you the same address every time.
You cannot circumvent this and somehow force a fixed IP address without cooperation from your ISP. Besides this not really being necessary, it is impossible to do through "a website or software".
Then, what do dyndns.org et al do? They claim something like this
This is another part of the internet: domain names.
Because ip addresses (the only way to differentiate one Internet connection from another) are rather difficult to remember and cumbersome to use, the DNS service was introduced. This allows an easy translation from a domain name (much easier to remember) to an IP address (the address that actually works).
But normal DNS (Domain Name Service) works rather statically. You register a domainname and your IP address, so others can connect to your machine. Dynamic IP addresses become a problem with this. Everytime your IP address changes, you need to change your domain registration.
Some services (dyndns.org and others, just google) allow you to update your actual IP address very often and automatically. So if your IP address changes, it will update the registration, and your domain will still point to your machine.
Then why, won't this help in this situation: because bittorrent (like many Internet applications) does not use domainnames. They use IP addresses directly. So while this helps to have your website (using a domainname) behind a dynamic IP address, your bittorrent is not affected.
(but, as stated above, bittorrent works around this already).