Trippy Internet Connection

Both our desktop computers are connect to a Linksys Wireless-G Broadband Router (Model WRT54G) through network cables and the router is connected to the modem. One day, I start my computer up and the internet connection is fine, but when my sister goes to start up her computer, she gets no internet. So she goes without internet for a day. The next day, I find that her internet is working fine, but when I go start up my computer, my connection status is "limited or no connectivity," same as her's yesterday. The next day, it switches again, my connection is fine, her's isn't. I tried connecting her network cable directly into the modem and restart both the modem and computer, and for some reason, she either still has that status of limited or no connectivity, or it says it's connected, but you can't connect to any sites. When I switch it (connect my network cable directly into the modem) and restart both the modem and my computer, it's perfectly fine. I have no idea what's wrong. Let me know if you guys need any additional info. Thanks in advance.