Without a data plan you won't be able to access the web. If you have a data plan there should be a browser icon on the BB. If there is no browser icon you can try to resend the service books (options/settings > host routing table > click on the top entry and register).
As far as unlocking, you could get ahold of Adam at GSM PhoneSource - When Only The Best Will Do
and see if he is able to get it unlocked. Very reasonable prices and very respected on these forums.