You can't have more than one direct connection from the modem to a network device (the local area or LAN side of the modem). What you'll need is a router to go between the cable modem and whatever you want to share your Internet connection.
The rear panel of a typical 4-port wired/wireless router looks like this:
The cable that now runs from your model to the computer would connect to the "Internet" or "WAN" (wide-area network) jack. Your computer, your new powerline adapter, and any other wired device (up to 4) connect to the "LAN" jacks. With this type of router you also have wireless connectivity available as well if you want to use it. Routers without wireless capability are available, but they can be hard to find. Most people want the wireless connections for laptops, network printers and so on to avoid the need to run cables.
Wireless routers are available almost anywhere where computers or computer supplies are sold, and are in the $40 to $50 range. Online you can often find them for much less. They are very easy to connect, since they all come with a CD containing all the necessary software to automate the process, and a manual to guide you through. You may need to purchase another cable or two since not all routers and other devices include one, but they are inexpensive.
Once you have the pieces you'll have your network running in no time. Good luck, and thanks for using Fixya!