Alot of times, PS2's can be repaired, by replacing one of the small SMD FUSES, which is dead for various reasons.
But please note, if the replaced fuse blows again, right after you apply power, then 9 times out of ten your board is toast, or has been badly damaged, but you can check for any small solder bridges due to a possible failed modchip install, those can also can a fuse to blow for no other reason.
And NEVER ever bridge a fuse, please replace it correctly with the same type, part and value, if you don't you might end up with a fire in your house, or burn your hand when turning on the power, or something even worse.
Attached is a list all the various PS2 models that I have so far. (Except for the latest slim ones, but they are basically the same as V12, just smaller!)