Could you paste the output of sudo lspci -vvv and cat /sys/devices/virtual/dmi/id/bios_version somewhere?
I am currently running Ubuntu 16.04 4.4.0-8 kernel which works fine. The ubuntu backport of i915 from 4.6 to 4.4 which is present in 4.4.0-9 causes weird video issues. (upstream bug: https://bugs.freedesktop.org/show_bug.cgi?id=94593)
lspci -vvv: http://pastebin.com/raw/FUsMqPZz
cat /sys/devices/virtual/dmi/id/bios_version: 1.2.3
Happy to provide any other info as well, I love this machine to bits and would be happy if I could help other people enjoy it too.
sudo lspci -vvv : http://pastebin.com/79BfxQC4