to start with godaddy doesn't have a clue when it comes to hosting, their business is domain registration and they should have stayed there.
also, they most likely just want you to upgrade to a more expensive package.
just make a backup from your admin panel, if you don't have any MODs installed, that will backup everything, do a full backup. then go ahead and install the blog, using the same database but a different table prefix and you will be fine.
by the way, there is a blog MOD for phpbb, a couple of them, check out phpbbhacks.com for them.