I have been running Ubuntu Mate on my Toshiba L850D laptop. Within the past month, the keyboard and trackpad do not start on bootup intermittently and it is happening more frequently as time goes on even after updates. I end up having to use an external keyboard and mouse. I am not convinced that it is a hardware issue.
What happens if you run it from a live USB of Ubuntu Mate?
Do you have a different live USB you could try, PC Linux, Mint or Manjaro?
Something that could eliminate it as a hardware problem.