You need to check what is running in the background. I know some people running spybot are having issues getting online with some games. It's gotten rather bloated and restrictive.
Couple that with windows firewall, defender, uac, and possibly conflicting protections like dual spyware protection/firewalls + routers well, you get the point.
Like skuzzy said, if you are able to get online via the http protocol, changes are you are capable of playing ah2 but need to ensure it's not connection restrictions.
I was just at a persons house removing 5 different spyware / adware / virus protection applications that were keeping his FIREFOX from opening. Only IE would work.
Not to mention, his cpu was at 40% at idle!
Sometimes, surrounding ourselves in a big foam protective package is not living at all. Rampant paranoia or ignorance often yields new dual core systems running like dx2-50's (for you oldies out there)
AVG free, zonealarm personal and Firefox - use those and only those and you should be fine most of the time. Just don't click OK when you see popups when viewing pr0n or searching for 'cool screensavers' and shiet like that. If it won't let you go past with cancel, ctl - alt - del and end task on firefox...start new session when it comes back.
If you only runs those above (I personally think a hardware firewall built into a router is just fine and zonealarm is not needed) I think you should be good and will be able to launch ah2 without issue (now playing is another thing depending on your system too)