NOT firewall related!
At about 8 years old, it's a prety old computer. BUT, as ALL support for Windows XP ends in April, you MUST still install Windows 7 or any Linux distro on it. I have a 10 years old computer that run Windows 7 ultimate without any dificulty...
Using Windows 7 and a router, you should have no problem connecting as the required components are integrated in the OS.
That also hold true for Linux.
If you want to use the Chrome OS, it's realy a version of Linux.
Can you connect to your router or modem using an ethernet cable? Can you connect to the router using wi-fi?
The best solution is through a router as the router will then take charge of the actual connection to the internet. Also, the router will hide your actual computer from the internet: Only the router itself is visible.