Long story cut short: Changing the kernel from 3.8.0-19-generic that comes when you click Ubuntu 13.04 x64, to Ubuntu1304-x32-vmlinuz-18.104.22.168-generic from the dropdown list has killed my box.
Looking at the console, I see:
... Exec format error
kernel panic - not syncing: Attempted to kill init! exitcode=0x00000100
Here's a screenshot of the full window: http://i.minus.com/i6gk45afcv9tM.png
I setup a droplet for a friend and taking exact notes and all the things I'd learned, I attempted to setup a droplet identically. Same size, OS and region.
All went well except vsftpd and people on Ubuntu forums were saying that "500 OOPS: priv_sock_get_cmd" is kernel related, and the only thing I realised was different was that I accidentally chose 64 bit.
So, I took a snapshot (phew!) and picked the latest 32 bit ubuntu 13.04 kernel I could find.
I've not restored from the snapshot just in case any staff want to explore the error. But it would be interesting to know what happened and why it happened!
These answers are provided by our Community. If you find them useful, show some love by clicking the heart.
If you run into issues leave a comment, or add your own answer to help others.