Airport Express Ethernet WiFi bridging with 3rd-party wireless base?

Question

I want to use an Airport Express as a substitute for a very-long Ethernet cable. Essentially, I want to connect a device (say, a computer) to the AE using an Ethernet cable, have the AE connect to a base station (not an Apple device) via wireless, and reach the network (Internet) on the other side of the base.
A diagram of the desired goal is at http://img.skitch.com/20091111-1j7a61eka32jqntm217wwg7d3g.jpg
I'm baffled. Here is what I've done:
-Reset the AE to factory defaults
-Connected a laptop to the AE via the Ethernet cable. Turn off my wireless (to make sure I'm talking to the AE via wired connection; this confirms the AE Ethernet port is working.)
-Configured the AE (via the Ethernet cable) in a variety of ways (see below), restarted it.
(alternately)
-Reset the AE to factory defaults
-Connected a laptop to the AE via wireless (connecting to the default-named network the AE creates on factory default reset)
-Configured the AE in a variety of ways, restarted it.
(This essentially suggests the AE is fully functional and not failed; I'm successfully able to connect to and configure the AE after factory default reset either wired, or wirelessly.)
I've tried various configuration attempts, but the one that seems to get closest - but still fails the goal is this:
-On "Airport / Wireless" tab: Join Wireless Network
--(I've entered my SSID for my network in the Wireless Network name field)
--(I've selected WEP 128 for security. I don't think I should be using WDS, given what I've seen elsewhere about WDS only working with an Apple Extreme.)
--(Of course, I've confirmed the passwords match)
-On "Internet / Internet Connection", the "Connect using" dropdown is disabled / greyed. This appears to only be enabled when I select "Participate in a WDS network" in the Wireless tab - which (as I said) I don't think I can use.
-On "Internet / Internet Connection", the Configure IPv4 is set to use DHCP
On restart, the AE successfully starts - it get's its IP address, the FIOS base station sees the device and lists it as online, and I can transmit audio successfully from iTunes to the stereo via the AE.
BUT, configured this way, the Ethernet port is not providing network connectivity to the device attached to the AE via the Ethernet cable -- the same Ethernet cable that was moments ago letting me talk to the AE to configure it is now not active. When I attach my MacBook to this cable and open System Preferences and look at the Ethernet connection, it shows as not even having a cable plugged in; there's no Ethernet link / carrier present. (Until I do a Factory Reset on the AE, after which it works fine again.)
Note: My AE is about 2-3 years old. I initially / previously had this configuration working just fine after I first installed the AE (after much pain, I recall). But I recently had Verizon installed, and in the process they put in a new base station. I seem to not be able to re-create the configuration I had that was working before.
Note 2: I'm attempting to use the wireless base station supplied by Verizon FIOS, which supports a ton of connectivity options - though it doesn't list (and therefore I'm assuming doesn't do) Apple's WDS.
Note 3: When I had it working before, I could have sworn the AE was also acting as a wireless base station that I could see in my available wireless networks listings, and was able to connect to the Internet wirelessly through it - as if it was a repeater of some kind. This isn't crucial; but it could be helpful in diagnosis.
Note 4: I think I may have previously had the AE connecting via another device: I also have a Netgear WG602v2 that was connected BaseRouter---Netgear((( ))) AE---Device (where --- is an Ethernet wire, and ((())) is a wireless link). HOWEVER, I can't be sure this is how it was working; this may have been a relic from attempts to get it working originally several years ago. It is not essential.
What am I missing?

Answer 1

It sounds like you have an older 802.11 b/g AirPort Express, which as Duane mentions will not function as you would like.
The newer AirPort Express 802.11n has a function called ProxySTA which allows the device to join (according to the attached article) virtually any wireless network with an option to "enable ethernet clients".
While it is not possible to know whether any wireless network will be compatible with this feature, it has worked on a 2Wire and Netgear router that I've tried. Haven't tried Verizon Fios, so I can't assure you that this will work as you desire.
http://www.macworld.com/article/132754/2008/03/express11n.html
Another option might be to use a pair of ethernet powerline apapters, providing that everything is on the same master electrical circuit. In general, I've found the adapters to be more reliable and better performing than wireless, but of course, your mileage may vary. Post back if you need more info on this option.