Computer Connected To Internet, After Few Minutes Only Some Sites Can Be Accessed

Win 10, 64 bit - Asus VivoBook laptop
Computer connects to internet, connecting to any sites for some minutes (seconds sometimes), but it stops connecting to all sites, except Google.com and sometimes Youtube, stackoverflow...
1. Not browser related. It behaves the same for all browsers, for all applications. ESET antivirus cannot connect to its server to update signatures, Outlook cannot synchronize and send mails, nothing can go outside on the internet, except Google.com and what I also mentioned above.
2. I thought it may be a virus involved. I scanned all computer (using ESET) and nothing found. Then, downloaded AdWCleanner from Malwarebytes, run it and nothing wrong found. At the scanning end it has a Repairing options (Winsock reset and "other settings of their default values"). I pressed the button and restarted. First time, after reboot, I could stay and navigate on internet wherever I wonted. But, before that I did some other things, as will follow and I couldn't be sure that this last option did the trick. Anyhow, next time when I tried (only) it, I had similar connection problems. In fact, not connection...
3. I tried all sorts of Winsock and DNS resets as following:
netsh winsock reset - followed by reset
netsh winsock reset catalog - followed by reset
netsh int ipv4 reset reset.log - followed by reset
netsh int ip reset
ipconfig /release
ipconfig /renew
ipconfig /flushdns
ipconfig /registerdns
Sometimes, I could not find a rule to be sure it works all the times, my laptop behaves normally...
4. Tried to manually set DNS (8.8.8.8 - 8.8.4.4) - did not solve anything
5. Not router related. My laptop behaves the same at home and at the office, different routers...
6. Not antivirus related. I stopped its firewall and nothing changed. Windows firewall is taken by ESET.

I do not know what to try, anymore. Any idea would be appretiated.
Thanks in advance!

 

Are you connected by wifi or wired?

 

Wired! But similar behavior being WIFI connected...
All the time I can see "Internet acces" moving the cursor over the network connection of system tray. But almost all the time it stops connections to all sites, except one or two. Now I am connected and I am able to access this site from the problematic laptop... Wired connected.

 

The problem disappeared after I uninstalled ESET antivirus...
So, problem solved.

I do not know how to mark the thread as solved...