In your case, it seems that DNS (or Internet) is not working. I also got this error message, when my computer was missing all connectivity. For note, I have another computer where network works ok (since I'm remote connecting it), but I still get the error message above...
Here are instructions step by step to find out where the internet connection problem:
1) IP traffic
ping 8.8.8.8
In my case I had ethernet cable, but no interface up. I had to first check out the interface name:
dmesg |grep eth
That outputed the device had been renamed as "em1" on my machine. On your machine it's probably something else. After this I was able to raise up the network (depending on your network settings of course) for example by:
ifconfig em1 192.168.1.123/24
route add default gw 192.168.1.1
Run again ping 8.8.8.8 to determine whether it works.
2) DNS
If the above step worked, then you can determine whether DNS works.
ping ubuntu.com
If not, then you can set manually the DNS settings by editing on terminal:
sudo nano /etc/resolv.conf
and enter to the top:
nameserver 8.8.8.8
This is Google's name server. After this try ping and do-release-upgrade again.