MySQL server cannot start on CentOS

I cannot perform any operation in MySQL because it gives error of:

Starting Mysqlcouldn't find MySQL server

root@server2 [~]# /etc/init.d/mysql status
MySQL is not running, but lock file (/var/lock/subsys/mysql[FAILED]
root@server2 [~]# /etc/init.d/mysql restart
MySQL server PID file could not be found!                  [FAILED]
/etc/init.d/mysql: line 301: cd: /usr/local/mysql: No such file or directory
Starting MySQLCouldn't find MySQL server (/usr/local/mysql/[FAILED]ld_safe)
root@server2 [~]# /etc/init.d/mysql stop
MySQL server PID file could not be found!                  [FAILED]
root@server2 [~]# /etc/init.d/mysql start
/etc/init.d/mysql: line 301: cd: /usr/local/mysql: No such file or directory
Starting MySQLCouldn't find MySQL server (/usr/local/mysql/[FAILED]ld_safe)
root@server2 [~]# mysql -u root
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111)

File /etc/my.cnf:

root@server2 [~]# cat /etc/my.cnf
[mysqld]
user = mysql
basedir = /usr/local/mysql
skip-external-locking
key_buffer = 384M
max_allowed_packet=268435456
max_connections = 500
max_user_connections = 35
wait_timeout=40
connect_timeout=10
table_cache = 512
sort_buffer_size = 2M
read_buffer_size = 2M
read_rnd_buffer_size = 8M
myisam_sort_buffer_size = 64M
thread_cache_size = 8
query_cache_size = 32M
thread_concurrency = 8
server-id       = 1
skip-innodb

[mysqldump]
quick
max_allowed_packet = 16M

[mysql]
no-auto-rehash

[myisamchk]
key_buffer = 256M
sort_buffer_size = 256M
read_buffer = 2M
write_buffer = 2M

[mysqlhotcopy]
interactive-timeout

Searching in some posts, I found that some program may be arresting MySQL. Follows the command I checked:

root@server2 [~]# lsof | grep mysql
tailwatch 20718      root  mem       REG        3,5    206553    8922204 /usr/local/cpanel/3rdparty/perl/514/lib/perl5/cpanel_lib/i386-linux-64int/auto/DBD/mysql/mysql.so

And the command yum info mysql-server:

root@server2 [~]# yum info mysql-server
Loaded plugins: fastestmirror
Loading mirror speeds from cached hostfile
 * base: centos.aol.com
 * extras: centos.chi.host-engine.com
 * updates: mirror.lug.udel.edu
Excluding Packages in global exclude list
Finished
Error: No matching Packages to list

Other Information:

• there is no MySQL process running.
• CentOS version 5.10 (End).
• is a dedicated server maintained by hostdime. Since when it was installed I only needed to change packages once, which was for PHP update. And you had no problem. This is almost 7 months old.
• there was never a need for an update except for PHP (as I said, 7 months ago). Other than that there was never a need to update MySQL periodically.