Access Denied for root MySQL
Looks like your socket file is missing

When that happens, you must connect to MySQL using TCP/IP as follows

mysql -uroot -p -h127.0.0.1 -P3306 --protocol=tcp


Specifying the port number and protocol, this will connect to MySQL with or without a socket file.

I have suggested this method many times when mysqld is running without a socket file

NOTE: Restarting MySQL will bring back the socket file. Usually, starting MySQL when mysqld is already running is what usually cause the socket file to disappear. (See Is there anyway that I can manually create a PID for the MySQL instance?)