Be very careful when working on the power board as it contains dangerously high voltages, even when not connected to the mains . This is because capacitors can remain charged for some number of hours or days.
Take all normal precautions before working in this area. In addition, handle the board as little as possible.
1) Follow the steps above to remove top cover, then remove the two screws from the controller ports
2) Lift the innards out of the base cover carefully, making sure that you don't damage the ribbon cable that is attached to the controller ports.
3) Turn the unit upside down whilst holding the controller ports, then remove the screws from the expansion bay plate (not pictured, but it is the dull plate with holes all over it), and the bottom of the psu (power supply unit).
4) Next, pull the psu up and out of its connector socket, you will also need to free the on/off switch from its holding plate, by just sliding it out.
A very common failure, which seems to crop up on some of the earlier PS2 models, is power supply failure.
When switched on there is no life and often, the internal fuses (or sometimes the fuse in the power lead) blow.
Very often, the fault lies with a very simple component on the power board. The usual component is a diode, of which there are four similar ones. Often though, the same diode fails each time. This is the third of the largish diodes, arrowed in the following picture.
Check the diodes with a continuity meter. If it shorts then it has blown and should be replaced with a 1 Amp diode. You should also test the board fuses (the amount of fuses differs, according to the version of the console) for continuity as one (or all) of these can be blown by the over current. You may also have to replace the mainfuse in the power lead as this can go at the same time.