PS2 Slim SCPH 90001 - Won't turn on - Power Led does not light up. :(

Hi all.
I think this is a classic problem on the PlayStation 2, but I don't know how to solve.

He sent me some photos of the main Board, which shows what's missing a SMD component.
I don't know if he was the one who removed the capacitor, but soon I confirm that.
Does the absence of this capacitor might be causing the problem?

I appreciate anyone who can help.

 

Updating...
(I just talked to him now)

When there was the problem on the PS2, my friend opened it. He had lots of dust there. When he passed the brush to remove the dust, the capacitor came out and he tried to reset, but failed. He imagined that it would be cold solder.
But the capacitor was still there when the problem occurred.

 

And that is why you should not use brushes to clean electronics. Electronic contact cleaner or some form of pressurized air always wins in the end. Though it does indeed look like it blew up?

 

Today he will bring the PS2 so I try replacing the capacitor. In fact, it seems that it blew up.

 

lol what kind of brush was he using? Steel wool?

 

Looks to me like it's been in use somewhere humid.

 

I was searching my Ps2 scraps here and see other 90001 models. They all have the same problem.This should be common in this model of PS2.
Independent of the component that came loose on my friend's mainboard, what causes this problem?
Which component I need to replace?

The power supply of the PS2 is good, has been tested in another console.