Yes, the wire connecting the motherboard to the screen can pull loose at either end.
Most of the time I find that it pulls loose from the back of the screen. To fix this, you have to:
open the screen bezel
unscrew the screen
lay it down gently
push the connector in to ensure it's tight
place a piece of scotch tape or electrical tape on the wire to ensure it holds in place
reattach the screen and then test it by powering on the chromebook
If the screen still doesn't power up, it could be the other end of the wire has come loose. or it could be the screen has died.