For BitComet to work with automatic port-forwarding, the router needs to have UPnP function activated. You can enable it by accessing the Administrator interface. You need to check the manual of the router to see the process.
Additionally, BitComet needs to be configured to use UPnP and a port as well. Use the image below to see exactly how it's done.
Note: As you can see I have port 8525, but I recommend pressing the Random Port button until you get something above 30000.