If you are using cPanel, you can usually look under one of the Stats icons to see (or download) your raw access logs. From there you will get information on who has been visiting your site and the pages they requested.
Once you know the IP address of someone you want to block, you can then put that address into your .htaccess file so that Apache will then deny them access to your site.
The .htaccess file lives in your site root (and also there maybe a copy in your forum root). To make the block site wide, edit the .htaccess in your site root either via FTP or your File Manager under cPanel.
cPanel also has (usually) something like an 'IP Deny' icon to do this as well, but since all it does it just edit .htaccess anyhow it is easier to do it yourself directly.
You may also like to look into the recent discussion on this forum about using a cache on your forum, like jpcache to help deal with high levels of guest traffic.
http://punbb.informer.com/forums/topic/ … for-punbb/
It won't block the attacker but may help your site perform better under stress.