Your best bet at your skill level is to email your host.
Upload your files back into the proper structure with FTP, I'm sure you know how to do that. Then upload your database dump to any old folder.
Create your new database, and email your host with the database name, dbusername and password, and ask them if they'll help you out by importing the dump that you've uploaded. It will take a competent tech about 30 seconds to do via shell instead of you trying to manually import it using something like MySQLAdmin.
Otherwise, have a look here:
http://www.vbulletin.com/docs/html/m...yadmin_restore
And here:
http://www.vbulletin.com/docs/html/m...tabase_restore
Once they've imported your database into the new one, all you'll need to do is edit your config.php to reflect the path change and new database name/password.
It's a very basic customer service request and honestly if they won't take a moment to do it for a paying customer, you should look for a new host.