There could be several reasons for MySQL not starting up and showing “MySQL daemon already running with the same unix socket” when trying to run it from the terminal.
The few times I have encountered this problem it has been after the server or VPS was improperly shutdown after a power failure or a forced shutdown on a VPS.
Both times there was a leftover mysql.sock located in /var/lib/mysql/ due to the improper shut down. Because of this mysql.sock file MySQL actually thinks that it is running when in fact it isn’t.
Delete this file and start MySQL back up.