Please help!
I think as a result of installing new Intel graphics software on my ubuntu-mate 16.04 lts system I get a black screen after the grub menu.

I created a live boot-repair disk and ran it twice.

This is the output
http://paste.ubuntu.com/23731363/

I also get a nearly full partition error message on my sda3 partition.

Prior to trying boot-repair I also added nomodeset to my grub menu but when I tried
I get an error
Question> can I uninstall software on my primary boot drive from a live usb?

Looking at the boot information script that you posted on pastebin: your problem is that no boot loader is installed in the MBR of /dev/sda.

Your best bet is to install Grub from a live CD or Live USB.
http://howtoubuntu.org/how-to-repair...ubuntu-live-cd

You have multiple posts for the 'same problem'. Kindly stick with them instead of making more threads.

-::-Reading the documentation of the distribution that you are about to install will educate and help you so you don't any troubles with your os.-::-

ok thanks. But if this IS the issue (I have 2 separate SSD's one has Windows 10 installed so I am wondering if boot-repair was confused?)
how does a boot loader suddenly go missing?
I need to know for future reference and hopefully prevent happening again

this is more or less a duplicate of
https://www.linuxquestions.org/quest...nu-4175596591/

and also
https://www.linuxquestions.org/quest...ly-4175596656/
is in the same vein.

please don't install software from the wild web.

reinstall, stick with the defaults, until you learn a little more about linux.

When the kernel gets an upgrade and one doesn't update Grub.

A bootloader will also go missing if the bootloader is not installed to the MBR.

Your boot repair output shows that you have Ubuntu installed using UEFI/GPT. When using UEFI, you do not need nor should you have any code in the MBR. The BIOS needs to be set to boot UEFI and it will then look to the EFI partition. Your boot repair output shows a 1TB drive on which you have Ubuntu and a 120GB drive which looks like it could be a Live Ubuntu system. The only possible sign of windows is the messed up partition sda4. Was that a windows or is windows on another drive? The efi partition on the 1TB drive shows only Ubuntu efi files although there are references at the bottom of the script to windows EFI files. With windows, you do need to use UEFI if you have GPT partitions. You might get a better understanding of this at the Ubuntu documentation site below.

https://help.ubuntu.com/community/UEFI

Thanks. If I've messed up the partitioning, just curious then why everything was fine for several weeks. Could my full root partition have something to do with my issue?

A full root partition will almost always be a problem to boot. You could use a Live DVD/flash drive to mount sda3 and see if there are directories/files you can remove. You haven't clarified where your windows is/was. The only possible partition for windows would be sda4 but there is no way to know if that was it. Did you have windows on another hard drive? If you had windows on another physical drive, did you have a separate EFI partition on that drive because there are no windows EFI files showing on the main (1TB) drive although they are referenced in the boot repair output. You also have an entry for windows in the grub.cfg file on sda3 showing it on "/dev/nvme0n1p2" which would be an SSD drive. There is nothing in the boot repair output showing this drive.

You're using GPT on the 1TB drive so you need to have your computer booting EFI for windows. Have you set the SSD to first boot priority as suggested at the bottom of the boot repair output?