This is called a paging file, and most installs will have it by default. This should in no way replace ram, unless you like wondering wtf everything is so slow.
Now, on topic:
Just because there is a computer on Ethernet does not mean it has priority over the wireless, unless some kind of QoS was setup on the router. Also, you seem to think your FPS in a game is effected by your internet speed? What game are we talking about? I highly doubt your connection speed is the issue. You probably need a new GPU, or in the case of OSRS a new CPU (OSRS does not use the GPU).
As for the networking, you can only have one modem hooked in a typical setup. This is because the modems MAC address is used by the carrier to identify your house and the service it gets. Without spoofing the MAC address (and this would be silly) you would need to pay for another line of service.
You're looking for a router I assume, which is either built into the modem (combos are popular these days), or connects via an Ethernet cable to the modem. This is usually the wireless AP as well. Wireless bandwidth is much less than ethernet (As low as 20Mbps with G, even though its 54Mbps in theory), so this could cause slow downs compared to a wired connection. But as I said above, I doubt the limited bandwidth is your real issue.
Edit: Seeing as you have a 2.21Ghz dual core processor, I assume you are playing OSRS and are having these FPS issues. Its time for a new computer :x That processor is 10 years old!