Help! Fixing an ASUS ADP-90YD BA, DAP013CA based power adapter.

[Watth]

Hello EEVpeople,
My DAP013CA based ASUS laptop power adapter stopped working.
After opening it, I got rid of as much silicon filling as possible, and could not see any obvious damages, except for the largest capacitor, which is slightly bulged.
So I thought I might start by replacing this one.
My humble DMMs don't have capacitance measuring features. Would a crude Arduino-based set-up be enough to test it?
If this capacitor (Nichicon PZ series 100µF - 450V - 105°C) has indeed failed, I'll see what replacement options I have in another episode.

To be continued...

[Watth]

Update.

A precision:
Before it stopped working completely, the symptoms where overheating, and it only worked if plugged to the PC before plugging it to the mains.

I replaced the cap with a new one with the same ratings (Rubycon 450TXW100MEFC18X35 http://uk.rs-online.com/web/p/aluminium-capacitors/7260754/?sra=pstk http://docs-europe.electrocomponents.com/webdocs/0f2a/0900766b80f2a1cd.pdf).
I have since acquirred a DMM that measures capacity. The old cap I removed (rated 100uF, and that was very slightly bulged) reads 95uF. So I can't confirm that it was the cause of the failure.

When plugged to the mains and without load, I measure about 19.5V, but is slowly declines. Is it because of the absence of load? If I unplug the mains, the measured voltage keeps dropping, until i show 19.5V again.
I don't dare try it directly on the PC...

I finished removing as much of the silicony paste as possible, and could not see any obvious hint of what failed.
The PCB is one sided and inhabited by TH and SM components.
I attached a picture of the board, and an annotated one indicating what's on the other side. I can, of course, provide more info about the components.

What can I do ?

[Armadillo]

Unloaded 19.5V seems normal.
Probably the heat is due to poor solder joints. See picture, cant tell if its reflection or poor solder joints.
Check continuity of the cables at both ends etc...

[Watth]

Nope, the solders are fine.

[coceicr]

Very strange schematic...
Here must replace C2 and C3 - 470nF/450V
When are bad (low capacity) the main voltage are increasing above 500V...... and the IC goes into protection.
https://4ham.ru/remont-bloka-pitaniya-asus-adp-90yd/