Yeah, I don't know what to tell you, unless maybe you're using SuSE Linux. I also have a BEFW11S4 and an E-machines laptop, and they work beautifully together. The only snag I hit was when I put SuSE Linux on it and it took a long time to resolve DNS names. I had to tell the OS not to use DHCP for nameservers, and specify which ones to use. That made it all better.
The Broadcom wireless client for Windows does a good job of handling the connection (much better than XP's Zero Config Service), so make sure that's running (it is by default). Other than that, maybe check to make sure your IEEE 802.1x Authentication is disabled, assuming you're using encryption.