My issues with MySQL update

[Brent Clark]

Hello all, I need your help please.

I updated our centos server 6.8 Final to the new version of mysql. Its not gone well.

I followed over the How to upgrade MySQL 5.5 to 5.6 on Linux

I did take a copy of my DB files.
I know my webserver files are still intacted
I have lost access to the Plesk GUI but still have ssh access.

Mysql is nor started and I get the following

service mysqld start

MySQL Daemon failed to start.
Starting mysqld: [FAILED]
[xxx@name ~]#


Some more info so you can maybe help

[xxx@name~]# mysql
ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (111)

Can any of you help point how to fix please?