I did this myself not a week ago. The laptop still works.
*Be sure to remove your battery and power so it doesn't start by mistake*
You have to take the plastic panel of your lcd off. It has 4 screws, under the little rubber standoffs. Use your fingernail or a flathead to get them off. Remove the screws with a Phillips screwdriver. Take a jewelery flathead, gently pull away the plastic border. You will hear little pops. This is the snaps undoing themselves. I start in one corner and make myself around.
Until it is like so:
(this isn't your exact model, but all Satellite LCds are configured the same)
Be sure the big white wire connects firrmly to the motherboard. should be on the side your VGA output is. I do not think it is under your keyboard.