When you rebuilt the droplet, it actually removes everything and installs whatever OS you've chosen. When the rebuilt is done, it sends a new root password to you - use that, not the one when you created the droplet initially.
EDIT: Unless you're using SSH-keys, then you don't receive an email with password.
This is a problem when you have configured SSH-only login, isn't it ? Since you lose all your data in the droplet when rebuilding, you also lose the part of the configuration where it says SSH-only. You then need to enter a root password when trying to ssh again. Since this password is a new one and DO didn't send it to you by email, you are stuck outside of your droplet.
