OSX El Capitan, DNS issue
The very first thing to have tried would have been to change from your provider's DNS servers to a known public one.

Google is one of the most commonly known - also the numbers are easiest to remember

System Prefs > Network > [currently used] > Advanced... > DNS

The number currently in there will be the one assigned by your DHCP server, i.e. your router, so you don't really need to remember it, but write it down if you wish.  

Hit the - button to remove it.
Hit the + button &amp; add 8.8.8.8
repeat &amp; add 8.8.4.4 
OK
Apply

Reboot &amp; test.

DNS issues usually sort themselves out in a day or two so if it works, keep it for a while, then swap back to your ISP's servers. You should be able to do that by simply removing both the Google servers &amp; hitting OK, Apply. It will find the right one from DHCP.