nice.
anyways it sounds like your display manager divorced your DE.
this happens
in budgie there is some blah blah && reinstall precise command...in Mate? don't know.
you have a terminal which is a plus
Solus says (https://help.getsol.us/docs/user/troubleshooting/) in case of DM issues:
"Display manager won't start
A common cause of not being able to boot is due to installing the NVIDIA drivers, but not booting into the latest kernel (the only kernel which has the drivers installed). Also ensure you have the correct driver version installed for your kernel. You can check if you have booted into the latest kernel by comparing the installed package with the booted kernel (instructions for both kernels)
eopkg info linux-lts | head -n2; uname -a
eopkg info linux-current | head -n2; uname -a
If the kernel version and release don't match from lines 2 and 3 of the output, then you aren't booting into the latest kernel and this is the likely cause of X not loading (particularly if you just installed the drivers). A couple of common reasons are:
On a GRUB machine, a common cause for not booting the latest kernel is due to Solus not being the boot loader on the MBR. Make sure you are booting via the Solus boot loader (if possible), or update GRUB on the distro that own the boot loader, see Legacy/BIOS installation.
Another possibility is that the ESP has run out of space so the kernel cannot be copied over to it. You can debug why this isn't happening via sudo CBM_DEBUG=1 clr-boot-manager update. This will output all information on the process, where it may be failing, or that it is working correctly.
If these two steps fail, you can't revert the installation of the drivers via History and Rollback"
now....also general boot rescuse page (https://help.getsol.us/docs/user/troubleshooting/boot-rescue) which should have commands to check broken and reinstall broken and sometimes chrooting and fixing boot (A BIG PITA but effective) fixes everything.
good luck you have a little troubleshooting to try.