Changed host, site not working

I was using Host Gator, and moved to 000 Webhosting. They both use cPanel, but different versions I believe. I exported my database using phpMyAdmin, and backed up all of my files on the server. While trying to import my old database on the new host, I ended up getting an error: http://imgur.com/Lvglhjt

I uploaded all of my files, but after I went to the site it asked me to set up WordPress again. I did that, and I got a million and one database errors, and it sent me back to the installation page again.

I am not too familiar with databases, but I watched a video and a guy had to click on the top so that it gets all of his databases. I might not have done that. 2 tables is all that showed up after I tried to import the sql file. Seems how I did a “full backup” on Host Gator, I was thinking that I could try and go through that and restore a different version of the DB. I heard that “full backups” actually do store the sql file, but I can’t find it. I really do not know if that would help, but I thought that I could try.

Does anyone have any suggestions?