Thanks to the help of @psyborg I can finally finish the main quest and access the veteran content. Here is his post:

psyborg wrote: »

I GOT THE FIX

proably u didnt finished the guild quest before. I reseted all my open quests and did the guild quest again (only last step dont worry).

after that main story worked again like a charm

Since I accepted the quest "The Weight of the three crowns" all the previous quest I had in my journal got bugged. The NPCs don't speak anymore, I can't use the required items for certain quests, etc.
I managed to fix all of them by abandoning them. But I can't get the quest of Selene's Web to work, the NPCs just talk and I can't do anything. It isn't really an issue (even tho I'm missing 3 free skill points...).

The real problem is... I'm completely stuck with the main quest... The NPCs don't move (I even waited one hour for them to do something, nothing happened...). There is no point in farming as I need Veteran materials to craft, the mobs don't give me xp anymore...

It has been one day, after several support tickets (all asking me to abandon the MAIN QUEST...), relog (which I keep doing), reload the UI, close the game for 15 minutes and log back in... But nothing helps, those NPCs just won't move.

@ZOS_GinaBruno and @ZOS_JessicaFolsom I request your help, maybe you have some insight on this situation.