I finally got wireless working on my Dell laptop under Linux. It turned out my Linksys 802.11g PC card was v2 which uses a TI chipset rather than Broadcom. Installing the v2 Linksys driver with ndiswrapper got it working.
One annoying thing about Linksys and many other network hardware manufacturers is that they often use very different chipsets in the product while using the same model number. You can only tell by the serial number or version which one it uses. The WRT54G is especially notorious for this.