Before my iPhone I had a Blackberry Curve with WiFi... I expereinced a similar situation at some hotels (never tried it at an A/C). I'm afraid I cannot remember the exact wording, but I recall using an option in the WiFi Setup where you could "sign on" to a network. This was useful in locations such as a hotel where (even with "Free Wifi" you have to sign on to a special home page and agree to terms or put in a room number.

Essentially, your BB thinks it's online because it's got an IP address... it doesn't know that the IP address that it has is not "enabled" (for lack of a better word) by the system. That IP address will be "enabled" once the system is told that you have signed in on their web page. Your carrier's Blackberry Support line may also be able to help walk you through the process. It's not the most intuitive, but it can be made to work.

Dave