In that case, I suggest you check the phpBB directories/files to see if any of them have been changed (particularly the phpbb configuration files that define the the database connection).If it seems that those files have been modified, you can always try replacing them with copies from the .snapshot directories (DH automated backups) from a time before the error presented itself.
If you have confirmed that the database connection information is , in fact, correct and that the site's files do not appear to have been "hacked", then there is really little more you can do without "shell" access.
If you are a programmer, you might upload some test scripts to attempt to connect to the database, but I'm not thinking that will provide much more useful information.
It is possible that the database server your site's forum is being server from is just "down" and needs to be restarted. Hopefully, if that is the case, another user of that machine might report the problem and DH's fixing that may solve your problem or DH's monitoring might catch the condition.
As a last resort, you could try posting the detail from your previous two messages here (make sure you include that you are an FTP user, and provide your user name) in a message to DreamHost vis the contact form at http://dreamhost.contact.cgi.
While not as good as a support ticket filed from the panel, it should eventually get to the right place, according to information posted on these forums by DH staff.