Just created new WordPress on Ubuntu 14.04 Droplet - after rebooting, MySQL won't startup and fails on manual startup. How to make it work?

I just created a new droplet, changed the MySQL root password and restarted the server with the reboot command. Now, MySQL isn’t running, and when I try to run it, I get this:

 * Starting MySQL database server mysqld  [fail]```

So I tried checking the status and I get this.

```# mysqladmin status
mysqladmin: connect to server at 'localhost' failed
error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!```

Any ideas here? This is a brand new droplet with minimal modifications. All I've done is upload some files into ```/var/www``` and configure and startup one vhost. 

Thanks.