Internet connection keeps dropping

I'm currently running a Power PC G5 (Mac OSX 10.5.8) and every 20 minutes or so (while browsing of course) my internet connection drops. Now, it doesn't appear to be a router problem because all other devices in the house (Apple TV, Ipod Touch, Ipad, PS3, etc.) have a strong wifi signal and work properly. When I go into the Network settings and check the Diagnostics, Ethernet and Network Settings appear as "Green Light", but ISP, Internet, and Server all appear as "Red Light". During this time, Safari pages won't open, Itunes radio won't load, etc.

Not sure if this may have something to do with the Network Location, Configuration, etc??? Nothing has changed recently, it just began cutting out about two weeks ago. I was thinking it may be the actual wires connecting the modem/router to the Mac's tower??? Not really Network savvy, so I didn't even know where to start...

Any help/advice would be appreciated!