There are two different settings you need to think about - one is for the IP address, and the other is for the DNS address. Automatic DHCP (default) will set both. Your other choices under the IPv4 Settings tab, are:
Automatic (DHCP) addresses only, which sets the IP addresses via DHCP, but allows you to set the DNS addresses yourself, in case you want to use an alternate such as Google or EasyDNS, etc.
Manual, means you set both the IP address and the DNS address. This may be what you selected, and so you have an IP address, but you cannot use domain names, only IP addresses, to connect out, since DNS translates the names to IP addresses.
Under "DNS servers:" in the IPv4 Settings tab, you can enter any number of DNS addresses, separated by commas. For example, if you wanted to use Google's public DNS servers, you would enter 8.8.8.8,8.8.4.4. If you want to use the same ones as your Windows system, you can check them under Windows using "IPCONFIG", or if you have the original Default network profile (you should), you can switch to that, then enter nmcli dev list iface eth0 | grep IP4 at a commandline prompt, and get the DNS addresses (usually 2).
Another way is to look into whether your router can assign static IP addresses. I find this to be easier to maintain.
Also, if you're worried about router security, you can probably simply disable external access completely. Most people never use it anyway.
Best Answer
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
and change the name-server to your router's IP address as
nameserver 192.168.1.1
Now restart your computer and test again.