Unstable internet connection and Safari/Firefox do not load
I'm trying to help a friend who has an iMac G5 running OS 10.4. with an ethernet connection and a Netgear router. AT&T/SBC is her ISP. She had no connection to the Network at all but I've didled with the settings including re-installing the router software. Now, she has an unstable connection to the Internet but neither Safari nor Firefox will load any site even when everything says it's connected.
When I run Network, Assist Me, Diagnostics, all lights are green. The modem will then occasionally flash red and lose the Internet connection even while I'm looking at Network Diagnostics showing all green and connected. Then the modem will find and return to solid green for Internet. Throughout all the solid green connections, Safari/Firefox will not go out and find and load any bookmark or new site. I assume I've missed something in the Network settings that's causing the instability and failure to run a browser.
Any suggestion to correct the Network settings would be appreciated. I assume that will fix the browser problem. Thanks.
BTW- She says it started when AT&T/SBC announced they were making email connection changes this month but I'm uncertain how that would change her ability to connect to the Internet. I think they're separate issues. Hopefully, I can fix the email problem (settings) when the Internet issue is resolved.
iMac, OS X Mountain Lion (10.8.4)