Having issues connecting to internet after CenturyLink fiasco

After the CenturyLink nationwide internet outage, my mac mini will connect to internet, but the thing is that I will start an internet browser, it will sit there for about five minutes looking up the site, then it'll tell me that it won't connect. Tried restarting, tried to check if it's the browser, switched between internet connections, turned AirPort on and off, all to no help. The Diagnostic won't help, and I'm frustrated. The Mac I own is a 2006 Mac Mini that is running 10.5.8, and it has always been able to connect to the internet. Please help! Every other machine works fine except for the mac. I don't have any idea what to do!