The central processing unit (CPU) in your PlayStation 2 is connected to the main circuit board inside the unit. Unfortunately, if you would like to upgrade the processor in your PlayStation 2 game console you will need to replace the entire board. The good news is that opening up your PlayStation 2 and removing the motherboard yourself is possible. It will take some concentration, but you should be able to complete the process in a relatively short amount of time.
Turn off your PlayStation 2 and remove any cables connected to the back of the device. Use your Phillips screwdriver to unscrew the box-shaped network adapter on the back of the device and remove it, if it's installed.
Turn your PlayStation 2 upside down and insert the tip of your flat-head screwdriver under the eight rubber screw covers located on the bottom of the unit. Pop them out of place to expose the screws underneath.
Use your Phillips screwdriver to remove all eight screws and set them aside. Turn the unit right-side up and lift the plastic frame of the PlayStation 2 from the back and remove it from the unit.
Locate the large square heat sink next to the disc drive of the unit. Remove all screws from the base of the heat sink.
Locate the controller and memory card port in the front of the unit and use your fingers to unplug and remove it. Set it close to the unit as it is still connected by a thick ribbon.
Locate the power plug port in the back of the device and then lift up the port itself and set it aside. Then lift the interior components (they are all connected) from the shell of the PlayStation 2.
Flip the components over and locate the square circuit board on the side of the unit. Remove all four screws from each corner of the board and then unplug the power port cable from the jack in the side of the motherboard.
Lift the motherboard out of the device and replace with the new one. These are available from your Sony retailer or online. Then reassemble your PlayStation 2 in the reverse order you took it apart.