I'm having problems with my ISP's DNS server. I'm able to do everything except visit any website using my browser through the website's domain name. I was with the technical support for 30 minutes trying to convince them that the DNS server was down but he kept on telling me there was an internet connection outage. I even explained to him that I was able to visit websites by using their IP addresses and by changing my DNS server to the Google's Public DNS server. He continued to tell me that the service was down in my area and that I had to wait 12 hours and call back. I'm also able to access other applications like Skype and such. So my question is, can ISP's DNS server go down and if so, why don't they know about it? Also are they able to reset my DNS to another server? Also what can and should I do in these situations?
EDIT: I was checking around the configuration of my router, and I saw that my DNS server settings were changed from automatic to static. Here are the servers IPs.
PRIMARY DNS: 184.108.40.206 SECONDARY DNS: 220.127.116.11
Is there a way I can figure out who changed these settings? I know it is not someone in my household. Could it be a hacker? How can I know where theses IP addresses are leading to? Is my network and it's traffic compromised? What other risks do I need to worry about?