Sorry, I don't know that answer well enough to give advice, but I was interested if you were switching away from Host Gator due to a dissatisfaction. I was planning to start using them in a major way very soon. This thread would be relevant:
http://www.webdesignforum.com/4759-hostgator-suspends-accounts-after-getting-money.html
1. Backup the current forum database.
2. Make sure that the phpBB that is on hostgator at the moment is the lastest version offered. If not update it.
3.Once updated, backup the forum database again.
4. Install a fresh copy of the lastest version of phpBB onto your new host.
5. Restore the forum database with your latest backup over the freshly installed phpBB that is on your new host.
Hope that helps and good luck!
1. Backup the current forum database.
2. Make sure that the phpBB that is on hostgator at the moment is the lastest version offered. If not update it.
3.Once updated, backup the forum database again.
4. Install a fresh copy of the lastest version of phpBB onto your new host.
5. Restore the forum database with your latest backup over the freshly installed phpBB that is on your new host.
Hope that helps and good luck!