Unable to connect to websites which don't start with www

What happens if you don't use a fully qualified domain name (FQDN), but, instead use an IP address in the browser? An example you could use would be http://208.80.154.224/. What you should see is a message stating:

Domain not configured

This domain points to a Wikimedia Foundation server, but is not configured on this server

Then what happens if you do use an FQDN for a website at that address, e.g., http://en.wikipedia.org/ or https://en.wikipedia.org/?

I've found it to be helpful sometimes when weird things like you are experiencing occur to check on what happens when I try connecting to a website using a telnet client rather than from a web browser. Sometimes that has helped me isolate the source of the problem. You can install a telnet client Microsoft provides or install the free PuTTY telnet/SSH client and then use PuTTY to connect to a website and issue a command that a browser would issue.

If you use Microsoft's telnet client, open a command prompt window then issue the command telnet example.com 80 (you can, of course, substitute any FQDN for a webserver of your choosing, instead of example.com). If you use example.com, type the following lines when connected hitting Enter once after typing the first line and twice after typing the second line. Note: you won't see anything from the web server when you connect to port 80 until you've entered the commands. You won't even see what you typed echoed back to you using the Microsoft client.

HEAD / HTTP/1.1
Host: example.com

The HEAD method requests information from the server, "HTTP/1.1" specifies that you wish to use version 1.1 of the HTTP protocol which supports specifying a host name, which is needed for servers hosting multiple websites. The "Host" line specifies the particular website you wish to access. You could use HEAD / HTTP/1.0 and omit the "Host:" line, but for servers hosting multiple sites, the "host:" line is the mechanism for browsers to identify the particular website they wish to access.

You should then see output similar to the following:

HTTP/1.1 200 OK 
Content-Encoding: gzip
Accept-Ranges: bytes
Cache-Control: max-age=604800
Content-Type: text/html
Date: Tue, 14 Mar 2017 18:11:44 GMT
Etag: "359670651+gzip"
Expires: Tue, 21 Mar 2017 18:11:44 GMT
Last-Modified: Fri, 09 Aug 2013 23:54:35 GMT
Server: ECS (iad/182A)
X-Cache: HIT 
Content-Length: 606

I don't know if you will get different results, i.e., be able to access sites without "www", attempting to access websites by that method rather than through a browser, but, I've found differing results sometimes, e.g., when a Windows system was infected with malware affecting access to sites via browsers on the system, though I wouldn't think malware would be the cause in your case, since the problem doesn't occur when you are using a LAN connection.

Another tool that can be helpful when troubleshooting connections to websites is Nir Sofer's free HTTPNetworkSniffer utility, which will allow you to observe traffic between web browsers on a Windows system and websites (example of data displayed by HTTPNetworkSniffer).