16.04 - Not able to get into console after presing Ctrl-Alt-F1

I'm just a happy man, who has just installed Ubuntu 16.04. So the problem is that when I try to load, I get GRUB CLI mode.

First question I do not understand why I see grub console instead of operating system list?

Ok, if I type exit in this console, Ubuntu continues to load and I get to login normal login screen. And here I face two problems

1. If I try to login using this login screen, I get into the system, but I do not see Unity components at all. Ubuntu just reports some error and suggests to send a report. And nothing happens. Just empty desktop and nothing else


2. I can not get into tty's by pressing Ctrl-Alt-F3-F7 - when I press it - I just see black screen and no login request.

I strongly suspect that this mught be related to my graphics card - GTX1070. But you know, I did nothing before - just installed the system and that it - it is already not working propely.

What am I missing?

Thanks!