The local default gateway (your router) will usually have an IP address looking 192.168.X.X. This is the bog standard LAN IP subnet, and each device (your PC being a device) will have a similar, but not identical IP. If this changes on a resetting of your router or passing of the set lease time, then that's the router's local DHCP at work. That being the case, and you have done port forwards, then they will no longer be applicable to the PC running BitComet, as the port forwards would apply to a specific LAN IP that is no longer addressed to your PC. A static IP can be arranged quite easily. See:
PortForward.com - Setting Up a Static LAN IP
It works something like this:
PC --> Router --> Internet
Your PC doesn't connect to the internet directly, when you're using a router. It's not a standalone modem, so things will be quite different. The router connects to the internet, and distributes the connection to your PC. So, in order for an application that requires a certain port or a number of ports to be open to work correctly, you would have to forward the ports from your PC (using the LAN IP that is currently assigned to your PC) to the router, and then the router does the rest in allowing traffic to pass through it to and from the internet. Furthermore, you should open the ports in any software based firewall you have running.
Now, this isn't required for all applications. Some are able to avail of UPnP, assuming your router is UPnP compatible. This is where the application automatically interfaces with your router and does all the required port forwarding for you. But I'll try not to confuse the hell out of you by going into too much detail, so I'll stop where I am now.
If you'd prefer, then check out
PortForward.com - Port Forwarding by Router for specific instructions on how to port forward based on your EXACT router, and the EXACT application requiring it.
May other guides, including how to configure software firewalls, can be found at
PortForward.com - Guides.
EDIT: I've just realized that these threads are dated 2006. I must've drank too much tonight! Oh well.
Seifer.