Well, I finally found the required torx t6 screwdriver and I opened the tablet.
Unfortunately I think it's the screen itself that's broken: reseating the connector made no change, heating (with the hair dryer) the mainboard had no effect, the only change I noticed when heating/cooling the screen alone.
Now I don't know what to do: change the screen (which is at least 100€) or use it as it is while it lasts.