Moving to a new server with no access to admin file

Background: A friend has been hosting my website (for free) for about 7 years.
The other day, I noticed it was down. They had changed DNS servers and told their paying clients, but not me.
I changed the DNS with my registrar but now my site (rubyfruitradio.com)says there is a database connection problem.
I would like to move my site to bluehost (where I have other sites hosted and have never had any problem), but I am not sure how to go about it.

Currently,when I try to get to the admin panel, I get the error “Error establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at localhost. This could mean your host’s database server is down.”

My friend is looking for database but doesn’t know what it’s called. I am not sure what database it’s looking for. I just want to move the whole thing because I am annoyed they didn’t bother to tell me they changed DNS servers and whenever something happens, it’s a pain to get it fixed. I would much rather have 24/7 tech support.

My question is this…How can I move my site to bluehost without access to the admin panel? All I have is access to the files via FTP. What is the easy way to do this?