After posting the last message, I poked around on SuSE's web site and found an updated pcmcia package. It's 3.1.15.
I installed and now have networking! However, I noticed a small bug?
Booting with the Linksys 10/100 Fast Ethernet card reports as a memory card, but the dmesg output otherwise look fine. I then remove and reinsert the Linksys and it's now a NE2000 and works fine.
If I boot without the Linksys installed, login, and insert the Linksys, it's now a NE2000 and works fine.
Maybe this is normal.
Anyway, I can use the network again without having to load modules.