OK so in the Main Quest I am at the sub-quest "A CORNERED RAT" and when I find Esbern he has no audible voice,and the subtitles are vanishing so fast I can't read them.
I reply to his questions and then he says he will open the door to let me in,but he doesn't open the door.
I'm stuck.

Try this, mate:
Stand in front of Esbern's door. Open the console (` key). Type "setstage mq202 160".
If it doesn't work, try some of the things outlined http://www.uesp.net/wiki/Skyrim:A_Cornered_Rat.

Go to the Skyrim directory then the data folder.

In there you want to extract "Skyrim - Voicesixtra.bsa".
The folder you'll end up with is "sound", place that into your data directory and it'll fix the issue.

As a point, you'll need to revert to a save you have that's BEFORE you try to talk to him.