When you updated the BIOS, have you tried to reset the BIOS settings too? Some will give an option to "Load fail safe defaults" or "Load optimised settings".
Equally, try running mate-settings-daemon from the terminal, to see if you can pick up any verbose error details on why it's crashing in the first place:
I think this might be a problem with monitor config . Have you tried changing the display settings after you changed the graphics card ? have you tried resetting mate-settings-daemon settings in dconf ? (sudo dconf --reset /org/mate/mate-settings-daemon)
I think @IvCHo is right, the graphics card or monitor is causing a problem with mate-settings-daemon. Concluded by this post from a quick search based on that error output. Since this fails to start, settings cannot be set.
The open source drivers (the default) could be the culprit here. Have you installed AMD’s proprietary drivers? (Word of warning: I’m not sure if an early bug is still present in 15.10 that prevents the system from booting with AMD’s drivers)
It seems to be a bug with MATE 1.10.2 - which Ubuntu MATE 15.10 uses. If need be, you could try Ubuntu MATE 15.04 or 14.04 LTS.