^ Good advice. PHPMyAdmin will almost always time out on decent sized databases. If you have shell access to your old host, run this command, changing the colored text to your info.

mysqldump --opt -u dbuser -p dbname > (path)/backup.sql

If you don't have shell access, ask the old host to do it for you - they almost always will. Once you have the output file created, you'll need to upload it to your new server and import it into a fresh database, using this command:

mysql -u user -p dbname < (path)/backup.sql

Again changing the colored text to your credentials. That will import your old database into your new database on your new host, and then you'll just need to edit config.php to point at the new database and you should be good to go if everything else (the files) transferred correctly.

Keep

--------------- Added [DATE]1223521611[/DATE] at [TIME]1223521611[/TIME] ---------------

What created the backup file? Did you just FTP everything down, or did your host create it for you? If you have SSH access to the old host you can dump the DB yourself. If not, as long as you haven't deleted your database on the old host you should have no problem getting it.

If you don't have SSH access to your new host, or don't feel comfortable, you SHOULD just be able to upload the dump file from your hold host to your new server and contact your new host to have them import it for you. It's a simple process and if their support is even half decent they should have no problem taking care of it.