Migration after server crash: maintenance mode and/or cache problem
Here is finally how I solved the problem with Yogesh help: when I tried to access the admin section while logged in as an administrator, I got an error. I therefore checked the watchdog table. The image_dimensions table was somehow missing:

[...] Undefined table: 7 ERROR: relation "image_dimensions" does not exist [...]


I created the missing table, and everyhting was then working (access to the admin section, access to the user section and so on).