CUPS service not working, can't find any logs

After a bit of searching and playing around, thanks to @Benjamin's comment above, I finally found that there is a default configuration file which should be installed in /usr/share/cups/cupsd.conf.default.

I ran

sudo cp /usr/share/cups/cupsd.conf.default /etc/cups/cupsd.conf
sudo service cups restart

and since then it worked!

I still have no idea how the file got lost in the first place though.

I ran:

sudo apt-get purge cups
sudo apt-get install cups --install-suggests

and then I checked that the configuration was correct. I still got a cups error trying to access a network HP printer, and I had to reinstall the printer, and then I got it to work.