Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)

I tried restarting the Mysql server but its not working for me. I am sure the server is running and the permissions on the folder /var/lib/mysql/ are correct (777). When i tried to open the file mysql.sock, its giving me an error saying the file may be corrupt. Please help me to log on to the mysql server.