Two thumbs up!

I just fetched my laptop, and it works like a charm!

Surprise: The problem was the connector! The computer hospital resoldered the connector to the main PCB. Apparently some of the solderings that been broken which explaines the intermittent failures. I paid about CHF 50.- for the repair, one fourth of what is usually charged in good ol' Switzerland to simply have a look and then tell you that "it's not worth to repair it - go buy a new one". So the backoffice did indeed know what they were doing.