1) Looks like RHEL6 prefers "mysqld"  instead of "mysql" for starting/stopping service (see below).
[root@localhost ~]# service mysqld restart
Stopping mysqld:                                           [  OK  ]
Starting mysqld:                                           [  OK  ]

2) Looks like your suggested login cmd returns good output (see below). What's the next step in this test drive?
Many Thanks,
Jenifer

[root@localhost ~]# mysql -uroot -ppassword
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 2
Server version: 5.1.61 Source distribution

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