Both pieces of LinkSys equipment caused problems, and I eventually decided to replace them.
While I was attempting to make WEP operate, the WAP-11 decided to re-configure itself, including setting the wireless MAC address to all zeroes! This is not a good thing (I don't know if there is some significance to an all zeroes address, as there is for IP addresses, for instance.)
It's behaviour was sufficient for me to upgrade the firmware. It came with version 1.009, and 1.01c was available from the web site. Upgrading is done via the web browser interface. As the other configuration program requires Windows, I have no idea whether it can also upgrade. I presume it can, but have no experience.
I downloaded the file from the LinkSys web site, and unzipped it. It recovers a file called linksys_nml.bin which I presumed is the file to use. Note that it has no version number, nor (an obvious) product name in the file name. And there are dire warnings that replacing the firmware with that for another product may render the AP useless. It'd be a pity if they put some elementary checks in.
Upgrading the firmware was an interesting experience. Let's just say sufficiently interesting that I went and bought a NetGear access point! I uploaded the file (via the browser) numerous times, only to be presented with the upload screen again. This, I presume, means the upgrade failed, for some definition of failed. In addition to uploading the file, I hit the reset switch numerous times (and also discovered that it tended to jam in the reset position!), power cycled it, waited over night etc.
Ultimately the planets must have been in the correct alignment, because instead of getting the upgrade screen, the login message appeared! Hallelujah.
Alas, the new firmware was worse than the old, at least in the sense that I could not get the card to connect to the hub when using WEP. I've heard that 1.01d is out; perhaps that is better.