There is a link to a forum in your website's footer and I managed to use the Wayback Machine to see what was there. It returned
one result in 2018 which clearly shows a phpBB 3 forum, although I’m not sure exactly what version.
You should be able to, as Mick says restore the forum from the database alone. Basically all you need to do is create a database in your hosting account and import the data using your database backup.
Download phpBB from the download section and then use the installer. You’d need to grab the files from the version the database relates to ideally as using a version that doesn’t match with your database backup will cause issues so if you can find out exactly what version you have that would help us help you further. One thing for sure is it definitely wasn’t version 2.8.