So I got tired of my browser constantly gong back to the wrong page after upgrading to 17.10. I cam across this handy page: Ubuntu MATE always forces search start page in Firefox where an administrator advised to remove the package ubuntu-mate-default-settings. After a reboot I do not have the mate desktop. I get a desktop with a background on it with a mouse (the rodent not the peripheral) on it.
What have I done, and how can I get my desktop back to mate?
I'm a little confused by the description of the background your describing in the quote above. Do you have the XFCE desktop installed as well as Mate?
When you get to the desktop, you might try the key combination of Ctrl+Alt+T
That should open a terminal. If it does, you can easily re-install ubuntu-mate-default-settings by running the following command in the terminal
sudo apt install ubuntu-mate-default-settings
That should undo what you removed, and hopefully after rebooting your Mate desktop will be back to normal.
Ctrl-Alt-T actually would not open a terminal, which I found strange, but I was able to open one with a right click in the desktop, and I installed that package. I sent this cry for help after the reboot with no success. As far as XKCE, that does appear to be what this is.
When I entered sudo apt remove ubuntu-mate-default-settings in the terminal I received the following output:
steven@Inspiron-3542:~$ sudo apt remove ubuntu-mate-default-settings
Reading package lists... Done
Building dependency tree
Reading state information... Done
The following packages will be REMOVED:
mate-desktop-environment-core mate-gnome-main-menu-applet mate-screensaver
mate-session-manager ubuntu-mate-core ubuntu-mate-default-settings
ubuntu-mate-desktop
0 upgraded, 0 newly installed, 7 to remove and 0 not upgraded.
After this operation, 3,686 kB disk space will be freed.
Do you want to continue? [Y/n]
This tell me that if you removed ubuntu-mate-default-settings you also removed the mate desktop as well. See mate-desktop-environment-core, mate-session-manager, ubuntu-mate-core, ubuntu-mate-desktop in the terminal output.
You could try reinstalling these packages and see what you get
sudo apt install mate-desktop-environment-core mate-gnome-main-menu-applet mate-screensaver mate-session-manager ubuntu-mate-core ubuntu-mate-desktop
Otherwise it might be time to backup any files you wish to keep and reinstall.
Edit:
If your left with a desktop that you can no longer log into, you can boot your machine from a live session and transfer any files you wish to keep to a external drive, prior to reinstalling Ubuntu Mate.
This worked. I re-installed Mate and all is well. I still have to deal with the homepage hijacking though 
Thanks for your help!
These in particular are known as “metapackages”:
mate-desktop-environment-coremate-desktop-environmentubuntu-mate-coreubuntu-mate-desktopWhile it’s generally safe to remove them so you can uninstall packages (e.g. ubuntu-mate-default-settings) that you do not want or need, it seems that since the default settings were removed, it had configured itself to log into XFCE instead.
Or maybe it also (auto)removed MATE and its components, which shouldn’t actually happen in newer releases. You can choose which desktop to use from the login screen if this was to happen again.
It removed the Mate desktop. It was no longer an option fro the login screen.
Poor diagnoses on my part actually. The metapackages are the only things being removed. However, after letting sudo apt remove ubuntu-mate-default-settings run its course in a Ubuntu Mate 16.04 VM, login was no longer possible after a reboot. Failed to start session.