Title sais it all. Is there some bug? Also the subtitles that Esbern talks go awfully fast, giving no chance to read it in time. + no sound when he speaks. Need sum help here fast

Try to reload a previous save or restart the game.

I don't know if it will work, but try to open the console, click the celldoor and type in "unlock".

Leave the room and come back in twice, and the cell door should be open.
As for Esbern's dialogue, if you're on a PC, you can download the file of the dialogue somewhere.. if on console.. I have no idea.

You should have posted this in the Spoilers section.

Sorry m8, kinda new to this.

Tried to leave and enter twice, nothing happened.

Edit: Tried once more to leave the room and enter and the door was open. Thx alot guys.

Then you should try to reload the save, or if on PC use a console command that resets the Quest.

Known bug, google the quest name: That is how i found the fix. A tsa extractor or something. It fixed the problem for me.

This guy is totally bugged...