We had the same problem for my coppermine server. Everything was fine until the box had to be shut down several times because of airconditioning loss in the server room over the last 2 days! During the last reboot had the same:
'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)
We tried everything including: permissions on /var/run/mysqld/ , commenting out 'old passwords = 1' in my.cnf, checking for *.sock in another directory, etc...
Then, after looking over all of the different posts I renamed 'my.cnf' to 'my.cnf.old', tried to start mysql daemon again (wouldn't start...couldn't find the my.cnf), then I renamed my.cnf again, restarted - - everything was back up and running!!
Our conclusion is that the my.cnf file may have been corrupt due to the shutting down/starting up that ensued over the last few days (Damn A/C compressor unit kept freezin' up!!), and by re-copying it was corrected. Very strange.
But, happy not to have to run to the tape library and go thru a restore!
Yuk to that!