Open the terminal and type in the following
You should get replies not host not found or request timed out. I am assuming the 192.168.1.1 is your router's IP address.
If the above worked it means it's connected to the router. Next try ping google servers and see if you are able to
if that works you should be able to access the internet but if it doesn't there might be a problem with DNS. If so try pinging the IP address of google servers just to make sure it can be reached via IP address
(this is a google DNS server IP address which doesn't change)
If that works you have your answer... DNS issue. If it doesn't work then check the resolv configuration file to see what the default nameserver is set to and change it to your router. The resolv.conf (base) can be accessed by typing
sudo nano /etc/resolvconf/resolv.conf.d/base
and change the name-server to your router's IP address as
Now restart your computer and test again.