Try closing the laptop's display to force the laptop into Clamshell mode to see if you get anything to show up on the external display.
Sometimes you can log in blindly by typing the first character of a user name and pressing the "Return" key. Then type your password followed by pressing the "Return" key again to submit the password.
To me it looks like the built-in Display Assembly is bad (see lower right corner where the LCD panel looks like it is damaged). It can be hard getting video to show up on an external display when the built-in display sort of works.
If you get video on the external display then the built-in Display Assembly will need to be replaced, otherwise it is hard to say. You will need to have Apple examine the laptop to determine what is wrong.