In this situation, we suggest using the recovery environment to assess the situation on the Droplet and attempt to get it back up and running. You can enable and disable the recovery environment directly from the Cloud Panel. This is in the Recovery options available from your Droplet page. To use this, start with turning off the Droplet ( either through SSH/web console or from Cloud Panel / API ) and then use the Recovery option 'Boot from Recovery ISO'. The next time you turn on the Droplet, you will be able to access the recovery environment from the web console. You can read more about the using the recovery environment on this post:
https://www.digitalocean.com/docs/droplets/resources/recovery-iso/