My Kindle's screen recently broke and unfortunately it was out of warranty (and it was probably my fault anyway!). While amazon did offer to sell me a new Kindle at a reduced price, I wanted to keep my old kindle due to its worldwide free 3G web browsing capability. I ordered a new screen from eBay for around £40. Changing the screen was pretty simple and took about 30 minutes.
I made video of the process in case instructions would be useful for anyone. I meant to take lots of photos during the process, but I was a little pushed for time, hopefully what I did take will suffice. Remember you can click the images to see them in full size.
Step 1: Remove the back cover. It is held in place with small plastic clips. Use a fingernail or a spudger tool to slowly undo each clip. Be careful not to apply too much force as you may damage the plastic.
Step 2: Remove the 2 screws holding the battery in place, and then remove the battery.
Step 3: Remove the 2 screws holding the 3G card in place and remove the 3G card. You can detach the aerial connector if you wish, but this is not required and can be a little fiddly.
NB: If your kindle is not a 3G model then remove the 3G card placeholder. I believe this is held in place with a weak adhesive.
Step 4: Remove the 10 silver screws indicated in the picture below. Also remove the black connector marked in the picture below.
Step 6: Remove the 8 black screws holding the main circuit board in place, and then carefully remove the board by sliding it upwards and then lifting it out.
Step 7: Remove the 3 black screws holing the main chassis, and then carefully remove the chassis.