Have you looked at the Wi-Fi diagnostics on your device? Manage Connections -> Wi-Fi Options, Menu -> Wi-Fi Tools -> Wi-Fi Diagnostics.
You will also find there Site Survey, Ping and DNS Lookup. Very useful tools in working out problems. You haven't specified your Blackberry OS in your profile so it is difficult to be specific, but modern Blackberry OSs are designed to work with, and use Wi-Fi in conjunction with, a Blackberry Data Plan. You can use it without one, but it can be problematic as you are finding out.
My other Blackberry is a PlayBook.