> Is mysql-server installed and running?

Yeah, it is:

[root@localhost nagios]# ps -ef | grep mysql
root     25630     1  0 16:22 pts/1    00:00:00 /bin/sh
/usr/bin/mysqld_safe --datadir=/var/lib/mysql
--socket=/var/lib/mysql/mysql.sock --log-error=/var/log/mysqld.log
--pid-file=/var/run/mysqld/mysqld.pid
mysql    25692 25630  0 16:22 pts/1    00:00:00 /usr/libexec/mysqld
--basedir=/usr --datadir=/var/lib/mysql --user=mysql
--pid-file=/var/run/mysqld/mysqld.pid --skip-external-locking
--socket=/var/lib/mysql/mysql.sock
root     25800  9962  0 16:32 pts/1    00:00:00 grep mysql
[root@localhost nagios]#