Thanks for the update.
OK. That looks good but you still can't connect to the server from your local client.
The reason I asked for mysql being used for other applications, is that you may need, as a last resort to remove and then re-install mysql and mysql client.
Before going that far, let's see what your logs show.
Is logging enabled by any chance in your config?
Check by running.
grep -i "log_" /etc/mysql/my.cnf
Please post what are the values and if they are enabled (uncommented) or not.