One of my collegue kindly considered that my contact detail shouldn't have been in CiviCRM and decided to delete it.
As a result, the dashboard can't be displayed, and the /civicrm is redirected to the home page.
I can still access it by typing an url (not the dashboard, ie; the search) and it works fine (at least fine enough for what I have to do on the db).
The error message on the dashboard should be clearer than a redirect (eg. the Civicrm contact (#124) associated with your username ("admin") couldn't be retrieved, probably because it has been deleted. You can create a new one...)