/root/REDMINE being deleted is weird. A snapshot is a perfect copy of a Droplet so that file should have gotten carried over too. You can stop bash from trying to read the file on login by opening /root/.bashrc in your favorite text editor and deleting the cat /root/REDMINE line.

Is the new Droplet using a new domain name? The under construction page appears when you try to access the Droplet using a domain name that it doesn’t know about. Open /etc/nginx/sites-enabled/redmine in a text editor. You should see a line that looks like this:

[...]
server_name 1.2.3.4 domain.com www.domain.com;
[...]

Replace the old domain with the new one and restart Nginx:

sudo service nginx restart

You should then be able to access your Redmine instance.