It may be the Router or Modem also, but...
Make a New Location, Using network locations in Mac OS X ...
Is that Interface dragged to the top of Network>Show:>Network Port Configurations and checked ON?
The Interface that connects to the Internet, needs to be drug to the top of System Preferences>Network>Show:>Network Port Configurations and checked ON.
Then... Try putting these numbers in Network>TCP/IP>DNS Servers, for the Interface you connect with...
Seems some dveice is havimg problems.
Open console in Applications>Utilities, check the system log for the date/time of the last problem & the Startup right after that for clues.
click on the top line we want, Shift plus click on the bottom line we want, CMD+c to copy, then paste the text in a reply with CMD+v
A couple dozen lines should be about right, hundreds or thousands won't likely be readable.