bigpaws: from his huge quote i derived he installed the package, ran the mysql_install_db script and tries to change his root password on the mysql server, though he hasn't got his daemon running (missing mysql.sock is just not a spawned daemon.)
To be sure about it though:
icedtea do
pidof mysqld
as root in your console, and see if it gives any numbers back or not.
And as newtor suggested, locate the position of your mysqld_safe executable with his commands.
Xeon.