Theres zonealarm free version, zonealarm pro, and there full internet security with anti virus i think, which one do you have?
Ive got zonealarm pro and normally when it blocks anything ill get a pop up message telling me its blocked something and what it was and it will ask me if i want to allow or deny access, you click allow and all should be ok?
im not too sure because i dont play online games myself but it should be fine if you allow it
By the way have you noticed an improvement in loading times now that your rid of norton? (thats assuming you uninstalled it correctly)