Recent update killed DNS via router

Something must have corrupted your /etc/resolv.conf file, it defines what nameservers your system queries. I’ve seen NetworkManager do this on occasion, I guess it’s a bug or some other unforeseen consequence.

netupdate simply moved the existing one into a backup and added the right nameservers from your network configuration (in this case, dhcp)

Edit:
/etc/resolv.conf is simply a text file with the follow structure:

search yourdomain.com
nameserver xxx.xxx.xxx.xxx

search is not necessary but the nameserver defines what IP it queries, for example 8.8.8.8. Each nameserver is put on its own line so if you want to have Google’s DNS servers, it would look like this:

nameserver 8.8.8.8
nameserver 8.8.4.4