I think I got the problem when another computer connected to the router got the same issue.
Basically, my modem/router was bugged. There is a virus that performs DNS injection. DNS of my network adapter had been changed to 220.127.116.11, which in turn was redirecting all the traffic from my devices to the attacker's website.
So, I called the phone company and got the modem reset. Updated the settings. The problem was fixed.
If you have the same problem,
1. Check the DNS setting in your modem/router. You may need to log into the router gateway like HTTP : / / 192.168.1.1 or something.
2. If it is 18.104.22.168, you will have to reset the router.
3. Note that if you are bugged, you might not log into the router though. So, you cannot see the DNS. Probably, you should probably check in your system. For example, I do this Ubuntu,
~$ nm-tool | grep DNS
4. Reset the router. Before you start doing that make sure you have all the information, id and password for your connection provided by the ISP.
Once this is done, you can see Google and sister websites load pretty well.