I have stumbled upon the exact same issue! I upgraded from 14.04LTS to 16.04LTS about a month ago, and everything went very well. Recently, however, no dash or window border anymore!
I have tried, as suggested in several posts, to reset config:
dconf reset -f /org/compiz/
setsid unity
I tried to reinstall unity and compiz,
sudo apt-get autoremove --purge ubuntu-desktop compiz* unity*
sudo apt-get install ubuntu-desktop compiz unity
I have tried to remove config files from local user hidden dirs,
sudo service lightdm stop
rm ~/.config/dconf/user
rm -fr ~/.cache/compizconfig-1
rm -fr ~/.compiz
rm -fr ~/.Xauthority
rm -fr ~/.config/autostart
sudo service lightdm start
Similarly, I enabled the Unity plugin in CCSM but this is not permanent since, when re-opening CCSM, the Unity plugin appears unchecked, even when opened with admin. rights.
Sadly, all of these attempts failed in restoring dash and window borders. I guess this is an issue with compiz, the window manager, but I have no idea how to fix it. Any ideas welcome ;)