A laptop lid is designed with durability in mind because it is a major component of protection. Everything is secured beneath the lid and protected by its hard exterior. Some lids are flimsier than others and can be cracked if closed with too much force or dropped. A heavy object falling on top will damage the lid and possibly the screen. Duct tape is an easy fix for holding it together, but the real way to fix a broken lid is to replace it. Locate a lid online, or find an identical laptop to salvage the parts.
Disconnect the laptop from all power; remove the plug from the socket and take out the battery.
Turn the laptop to the back and locate the hinges near the bottom of lid. Use the screwdriver to take out the screws. There are usually two, but your model may have more. Place the screws in a baggie for safekeeping.
Turn the laptop to the front and locate the speaker panel above the keyboard. This panel will usually contain the power button and the model name.
Push the lid so it's completely open and use the butter knife to gently pry the panel up. You should see the bottom area of the lid exposed, with approximately four screws attached.
Disconnect the LCD cable from the motherboard; this is usually a thick cable located on the left side.
Remove the four lid screws and lift the lid away from the base. Set the base aside.
Use something pointy or sharp to pry out the rubber stoppers along the edge of the screen. There should be approximately six to eight stoppers, with screws revealed underneath each as they are removed.
Take out the screws and use the butter knife to separate the bezel (frame) from the screen. Place the bezel aside.
Take out the screws that hold the screen to the lid and carefully remove the screen.
Place the screen into the replacement lid and attach with the same screws. Replace the bezel, screws and rubber stoppers.
Secure the new lid to the base with the previously removed screws and install the remaining pieces in reverse order.
It will be cheaper if you purchase a laptop lid that does not contain an LCD. However, if your screen is broken also, get a lid with an LCD to repair both at once. In this situation, you'll only need to remove the broken lid and replace it with the new one without removing the LCD.
Computer parts are very sensitive to damage by static electricity. Lay all hardware on anti-static bags, if possible, and consider purchasing an anti-static wrist strap.