There is a bug in the A Cornered Rat quest in The Elder Scrolls V: Skyrim. When you find Esbern in the sewers, he won't open the door for you or speak (but you'll see subtitles if you have them enabled). Since this quest is part of Skyrim's main storyline, you won't be able to proceed without completing it. The bug occurs due to a mix-up inside the game configuration files. Solution:
1. Download SkyrimEsbernFix.rar
2. Extract its content to the game root folder.
There is no need to backup your savegames. The file above just includes all the missing audio files.