Working with someone on a new Mac Mini with Firefox and Safari loaded.  The router is Airport Extreme on DSL.  When clicking in to a new link, including Apple.com, we're often getting a 'cannot connect' message, and some of the time, part of the website may show up anyway below the message.  If we take out the tail of the URL, sometimes just the slash, it may work, or not.  The problem can show up in both Firefox and Safari, but not necessarily on the same sites.  Some sites we don't get to at all. 
I figure there is some setting to change, or a plug-in to trash, but I don't know what.  Thanks in advance for any help.

Are you able to test the Mini using a wired connection?

Is there another computer in the house that can connect using wireless?