ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

First make a backup of your /var/lib/mysql/ directory just to be safe.

sudo mkdir /home/<your username>/mysql/
cd /var/lib/mysql/
sudo cp * /home/<your username>/mysql/ -R

Next purge MySQL (this will remove php5-mysql and phpmyadmin as well as a number of other libraries so be prepared to re-install some items after this.

sudo apt-get purge mysql-server-5.1 mysql-common

Remove the folder /etc/mysql/ and it's contents

sudo rm /etc/mysql/ -R

Next check that your old database files are still in /var/lib/mysql/ if they are not then copy them back in to the folder then chown root:root

(only run these if the files are no longer there)

sudo mkdir /var/lib/mysql/
sudo chown root:root /var/lib/mysql/ -R
cd ~/mysql/
sudo cp * /var/lib/mysql/ -R

Next install mysql server

sudo apt-get install mysql-server

Finaly restart your server.