With the computer off:
Most of those units have a flat plastic piece between the keyboard and the screen, just above the keys. It is removed by sliding it sideways to the right about 1/4" and then it comes off.
Under that panel piece is the plug to connect the screen to the mainboard. That plug and socket oxidizes or gets a bad connection over time. Carefully pull that plug with about 20 wires connected to it and clean the plug and the socket with a 'Q-Tip' or tape head cleaner using contact cleaner or 99% alcohol. (Tape head cleaner works well too). Use a 'canned duster' blast to dry it and replace. 99% alcohol is not impossible to find. In the U.S. 'Safeway' Stores have it, but very few pharmacies.
Place the plastic piece back in position and slide to the left to click it back into place.