First, purchase your replacement LCD display for your exact model of Toshiba A135. I found mine for about $110 with shipping.
There are five screws hidden beneath rubber bumpers around the screen. Carefully use a small flat screwdriver to remove the pencil eraser sized rubber bumpers - one at each corner, with the fifth at the top center. Make sure you carefully remove the sticky stuff they used to adhere the bumper to the screw as well. Set these carefully aside.
Remove the five screws and set them aside.
Gently press down at the inside plastic frame until it pops out slightly. Gently press towards the center of the screen at the sides of the inside plastic frame until it pops out.
Carefully separate the front and back plastic shell around the screen. Set the front plastic frame aside. You may need to loosen some of the white tape used to keep wires attached to the rear plastic shell. Gently lower the rear plastic shell away from the LCD, but leave as many wires attached as possible.
On the back of the LCD there is a large cable. Carefully pull up the tape that holds this cable in place and pull the cable down to remove it. You will also have another piece of white tape on the back of the LCD to peel back. The tape is important - don't tear it or get your fingers in it to remove its stick!
At one end you will see a set of a few wires plugged into a piece still attached to the rear plastic shell. Unplug this.
No wires should still be plugged into the LCD anywhere at this point.
Around the LCD there are six small screws. Remove these and set them aside. You now have now removed the old LCD.
Reverse this process to re-assemble.
* You may want to use some blue LockTite (which can be found at hardware stores) for the screws as you replace them. Additionally, you might need a little rubber cement to re-attach the rubber bumpers at the last step. If you do not re-attach these bumpers, your screen will quickly become scratched by your keyboard touching it when the lid is closed.
Good luck!
