The one-click install is out of date (2 major versions if I’m not mistaken) and there have been a number of support requests recently that appeared to be related to the DO install.
Are you still able to access Discourse from the browser? If so, download your backup from /admin/backups. If not, the files are located (by default) in /var/discourse/shared/standalone/backups/default. If you can find the installation location in your droplet, the shared folder should exist and from there you should be able to get the backups.