The script that had been provided to you would work fine, provided you have the oratab, normally put under
/var/opt/oracle/oratab and make your database start option from "N" to "Y". This would start/shutdown the database during the reboot.

To kick in the listeners try

su - $ORA_OWNER -c "$ORA_HOME/bin/lsnrctl start"
or
su - $ORA_OWNER -c "$ORA_HOME/bin/lsnrctl stop"

This should fix the issue. If you need more information on this, there is an old thread that discusses, on this issue and also has a posting on the dbora file.

Good luck
Sam