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 ?