If the port on the cable modem and the Ethernet cable works with your other computer then you know its not the port or the cable. The only thing left is either the port is bad hardware wise or it is not enabled or recognized within Windows. The first thing to do is to open your network connections and make sure your local area connection is enabled. You can right click on it to check. You can also check in Device Manager to make sure your Ethernet network card is installed and enabled. You may want to update the driver if it is enabled and shows that its working properly.
If your Ethernet connection on the laptop has a link light make sure it is lit up and also lit on the port on the other end. It is usually green for a good link and amber for no link. Sometimes the port will only have one light and it may be amber for a good connection so be aware of that. You can also try plugging the laptop into another device like a router or hub and check for link lights to get a second opinion on the port. If it turns out that it is bad you can install an Ethernet PC card into an open slot and use it that way.