If you're using Windows XP you could give this a try:
Firstly, exit or disable any "connection managers" you may have until you are 'using Windows to manage your wireless network'. This just makes it easier for you to diagnose the problem. Now you will want to go into your Wireless Network properties (Right click on "My Network Places" from your desktop and you will see your Wireless Network Connection.)
Now, Right-click on your wireless netowk and go to Properties. On the first window that comes up, make sure that "Notify me when this connection has limited or no connectivity" (or something similar to that) is NOT ticked. Having this ticked causes a lot of problems.
Right, now try connecting using the Windows utility. You can load this from your "My Network Places" by clicking "View available wireless networks" and try connecting again.
Hopefully, if no other programs are trying to connect and use your wireless card, you should be able to connect. In theory, you don't need a BT connection manager or the Broadcom connector because as long as you can connect to the network, that's all that matters...
Hope this makes sense and helps you out a bit!