First, I would try repairing Unity using a script from this question
sudo apt-get install unity-tweak-tool
unity-tweak-tool --reset-unity
If all else fails
I would recommend that you install a different desktop interface, such as KDE (picked because it exists in the main repositories).
sudo apt-get install kubuntu-desktop
If you are able to login to this, then uninstall Unity (I have not tested this step)
sudo apt-get remove unity unity-2d unity-2d-panel unity-2d-spread unity-asset-pool unity-services unity-lens-files unity-lens-music unity-lens-applications gir1.2-unity-5.0 unity-common indicator-sound indicator-power indicator-appmenu libindicator7 indicator-application indicator-datetime indicator-messages libnux-2.0-0 nux-tools libunity-misc4 unity-2d-common
Commands from https://askubuntu.com/a/20065/89515
Reinstallation should be easier, with sudo apt-get install ubuntu-desktop