It is normal for heavy laptop users to eventually experience loose or broken laptop hinges. Broken plastic hinge covers can occur when a computer is dropped, when you try to troubleshoot a hardware issue or simply from normal wear and tear. Broken outer plastic hinges are a purely cosmetic problem but if the metal interior hinge is broken then this will keep the display from standing up and may eventually even break the LCD by falling. In either case the hinge cannot be fixed but must be replaced with a hinge made especially for your computer make and model.
Turn off the laptop and unplug the AC adaptor from the laptop. Remove the battery too, so you don't short-circuit anything.
Disconnect the laptop from the power outlet and take out the battery so you don't short-circuit the machine.
Turn the computer so the back faces you. Remove the screws that hold the back plastic hinges. Gently pry up the plastic hinges starting in one corner. Remove any broken pieces and loosen the hinges as much as you can.
Turn the computer so the front is facing you and open the screen as far back as it will go. Look at the area between keyboard and LCD screen to see if there are any screws and remove them with a precision Phillips screwdriver.
Lift up the plastic hinge from the back to the front until the front plastic plate above the keyboard lifts with the hinges. Replace with a new plastic hinge plate and fasten the screws in place, if this is the plastic hinge that is broken.
Disassemble the laptop as you did in Steps 1 through 4 of Section 1.
Remove the screws that are available just above the keyboard. These hold the keyboard in place and give you access to the metal screen hinges.
Remove the rubber stops in the display bezel and unfasten the screws there. Insert the flat edge of a flat-blade screwdriver in the seam of the front plastic screen bezel and the back plastic cover. Gently pry the front bezel from the screen to reveal the upper hinge holding the lower assembly to the upper. Remove the screws from the broken hinge. Replace with a new hinge.
Replace the screen bezel and other plastic parts. Connect the laptop to the power outlet, turn the machine on and use normally.