Is your router's wireless signal encrypted?

If it is connected and the signal is strong, then the driver should be fine. The problem is the settings.
Since you said you just installed XP, the wireless adapter should be in default state, that is, DHCP enabled, encryption disabled. If your router's wireless is encrypted, your wireless broadcom adapter has no way to connect.

Double click Broadcom Utility Icon on right side of the bottom taskbar. Do a scan(site survey). If your router is marked with a lock or labelled with WEP or WPA, your router wireless is encrypted. You need to turn on encryption in your broadcom adapter accordingly but you need to know the encryption key.

If your router was installed and configured by your Internet Service Provider, consult the ISP instruction or ISP customer service on how to get back the key.
If the router was configured by yourself or someone else, and your forgot the key, you have to reset the router and reconfigured the router with a new key. If you are clueless about all this, you really need to have someone come over to help ya. Gook luck.