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

* Stopping MySQL database server mysqld [ OK ]
* Starting MySQL database server mysqld [fail]

beloz@paper:~$ ps -ax | grep mysql
Warning: bad ps syntax, perhaps a bogus '-'? See [-link-]
7650 pts/0 S+ 0:00 grep mysql

beloz@paper:~$ ps -ax | grep inetd
Warning: bad ps syntax, perhaps a bogus '-'? See [-link-]
7653 pts/0 S+ 0:00 grep inetd

beloz@paper:~$ mysql_install_db
Installing MySQL system tables...
080408 17:26:47 [Warning] Can't create test file /var/lib/mysql/paper.lower-test
080408 17:26:47 [Warning] Can't create test file /var/lib/mysql/paper.lower-test
080408 17:26:47 [Warning] One can only use the --user switch if running as root

/usr/sbin/mysqld: File '/var/log/mysql/mysql-bin.000131' not found (Errcode: 13)
080408 17:26:47 [ERROR] Could not use /var/log/mysql/mysql-bin for logging (error 13). Turning logging off for the whole duration of the MySQL server process. To turn it on again: fix the cause, shutdown the MySQL server and restart it.
080408 17:26:47 [ERROR] Aborting

080408 17:26:47 [Note] /usr/sbin/mysqld: Shutdown complete

Installation of system tables failed!

Examine the logs in /var/lib/mysql for more information.
You can try to start the mysqld daemon with:
/usr/sbin/mysqld --skip-grant &
and use the command line tool
/usr/bin/mysql to connect to the mysql
database and look at the grant tables:

shell> /usr/bin/mysql -u root mysql
mysql> show tables

Try 'mysqld --help' if you have problems with paths. Using --log
gives you a log in /var/lib/mysql that may be helpful.

The latest information about MySQL is available on the web at
[-link-]
Please consult the MySQL manual section: 'Problems running mysql_install_db',
and the manual section that describes problems on your OS.
Another information source is the MySQL email archive.
Please check all of the above before mailing us!
And if you do mail us, you MUST use the /usr/bin/mysqlbug script!