Most laptop keyboards are screwed in from underneath to secure them and prevent them from coming away from the case. Inspect the bottom of the laptop for any missing screws. In specific, try to see if any of the screws on the bottom have a Keyboard label next to them. These will be the ones holding your screws down.
With regards to your display issues, do these issues appear when opening and closing the lid? They could point to the display cable coming loose from behind the LCD.