Forgot to add that the coffee shop assigned IP
addresses using DHCP (just as I do at home).

I hope you don't mind me suggesting this, I don't want to teach my
grandmother how to suck eggs,but I have this this mistake a few times
causing much 'angst'.
When I enter the key it is ASCII but the default on the drop down window
is HEX. Just check that you have selected the appropriate one.

The password is ten digits. I've tried passphrase,
ASCII and HEX. None have worked. The owner says that
the password is ten characters long and consists of
the phone number.

Frankly, I'm baffled. If I determine that my settings
are correct then I will move on (there are lots of
places with free wifi around). But if it could be
something on my side that needs tweaking then I would
like to troubleshoot longer. Is it possible that there
may be some setting on the coffee shop side that I
have not considered? (Assuming, of course, that the
owner has given me valid settings.)

I posted this as response to another wireless issue as well:
I've noticed that linksys will sometimes take a hex key and lower case
the key. When you put it in your system, my Dlink for example wont take
lower case. It assumes its all uppercase. My SGB modem though takes it
either way and keeps it how I put it in. Depending on what the coffee
shop has equipment wise, you might try all uppercase and all lowercase
in the key and see if that helps.

Also with wep codes ubuntu wants a dash after every 4th character. Not sure
if you knew that or not that is what was causing my issues for a wile there.

I'm beginning to think that the settings on my side
are ok and one of two things is wrong: Either I'm
missing a piece of software or there is something on
the coffee shop's side that I'm not aware of. In
either case, it doesn't look like I'll be using wifi
at that coffee shop.

There are lots of other places that offer free wifi. I
have successfully connected to open wifi sites (no
password and no captured web page requiring a key
stroke or two). I have also successfully connected to
free wifi sites that capture the web page and require
a few keystrokes before accessing the internet.

This is the first that I've found that requires a WEP
password (other than my own personal connection though
I now no longer use WEP). If I find another and have a
similar problem then I'll pursue it further. For now
though, I'll just won't use that coffee shop's free
wifi.