In order to take off the top cover, you need to remove the front face of the computer. To do that, there are the small plastic clips on the inside of the case similar to some Dells I have seen. Open up the side and find the three small plastic clips and push them in while slightly pulling out on the front face. The front will open like a door (one side swings a bit while the other side is free).
You also have to take off the other side of the case. In the case I'm opening today, this took a tremendouse amount of muscle. There were no screws holding in, but it took effort to remove it. In face, I had to take off the front cover and push the other side case with a flat head screwdriver to get it off, I could not pull it off from the back.
So in summary, this is the order I would use if I could go back in time:
Remove the two big black screws to get the main side door off.
Push the plastic clips near the front of the case in to take off the front cover.
Remove the two silver screws in the back holding the other side door on.
Push the side door off.
Remove the one screw on each side that is holding on the top cover.
Remove the two screws in the front and back that are holding on the top cover.