I am doing the quest A Cornered Rat and found Esbern in the Ratway. The trouble is, I can't hear him talk and he won't open the door. Is there a fix for this glitch?

This is a problem with compressed audio files not decompressing properly..
Download BSA unpacker:
http://www.tesnexus.com/downloads/file.php?id=3117#content

Use it to open the file named "Skyrim - Voicesixtra.bsa" in the Skyrim Data folder. (Right click, run as admin)

Click on "Extract all" and choose the Skyrim Datafolder as the destination.