It says just as you indicated "accessing iTunes store" endlessly. Before last night, I would just close the session and iTunes would close. I removed and reloaded the updated version last night. It still just sits in the endless accessing senario. However, now when I close with this current version, I get the message 11222 error. Not sure if it's similar to the prior issue or not, but I never got that message until I removed and re-installed the new version. I can connect using my other laptop, so this leads me to believe it's system related and not network related.
With those symptoms, I'd try the following document:
(If there's a SpeedBit LSP showing up in Autoruns, it's usually best to just uninstall your SpeedBit Video Accelerator.)