Turn off the PlayStation 2 and carefully unplug it from the power source. Also, it is important to eject the CD from the console before flipping the it upside down.
Once all of the screws have been removed, pry apart the plastic covers. Start by lifting the side containing the power cable and Ethernet port. Then, lift the opposite side to fully separate the two sides.
You may need to apply some gentle force to detach the covers. Be careful not to break the plastic screw pins.