Firstly pings make no difference at all to web browsing. I can connect to a site in china just as fast as one in england.
Secondly, not watched the video, but what time was it at? What browser? Either can make a huge difference - at peak times (evenings) this site is ridiculously slow. At this kind of time it's not too bad.
It's either you have a shit server or one that needs setting up better, or phpbb is reaching its limit. I'd say it's a combination of the two.
I don't think the server is capable of processing so many requests. There's probably a few "select * from" statements somewhere which are slowing everything down. Do you have a seperate database server?
I've said it before - Vbulletin is the way forward.