Launcher or top panel disappeared after update of Ubuntu 16.04

I'm running Ubuntu 16.04 on my desktop and have a big problem with Unity. After an update (February this year) I lost the Launcher, the panel on the top of the screen with the username, the time, language and all the other buttons. In addition, the shortcut Ctrl+Alt+T doesn't work.

I found some similar treats on some sites (e.g., askubuntu.com), tried the solutions there but nothing worked for me. I tried to install the Gnome environment but unsuccessfully. Finally, I managed to install Mate, but don't like it and it has some pretty serious bugs, e.g., when I add keyboard layouts for other languages, they don't work. Also Firefox doesn't work properly with Mate. In the last few months I was hoping that this issue will be fixed by some update but this hasn't happened so far.

Can someone, please, help me fix Unity? I don't want to reinstall Ubuntu. It will cost me a lot of time to back up files.