Are you on a home wifi network or wired network? If you find yourself without DNS, quickly go to CMD prompt and do a ipconfig /all. This will show if you still have an IP address and what your DNS servers should be. Take that DNS server IP and ping it. Can you hit it? Next try an "NSLOOKUP <dns ip>" then type in any site name like www.google.com and see if you get an IP address for resolution.
If your suspect your ISP dns, you can use any pubnlic one like 8.8.8.8 or 4.2.2.2
I would check to see if you have any additiona. devices in your house doing DHCP. PErhaps another device is serving up addresses but has bad dns info. Ipconfig /all will also give you the dhcp server from which you acquired the address.