Well, I found the answers to my own problems. Here's what solved things in my case:

1) One of my laptops was out-of-date on it's BIOS. There was a new update available, which specifically did something with CardBus support under Win2k. So, I ran that.

That didn't fix the problem by itself -- here's what else:

2) The WaveLan driver that was installed on my system was the one that Microsoft bundled with Win2k, not the Lucent driver itself. I removed the MS driver and put in the Lucent driver.

Voila. Stumbling on both laptops now.

Good luck to all,

-Toomer