No, it's not "impossible" for it to fail. As a professional network geek, I see WNICs on a weekly basis that don't work. They _think_ they are fine, but they just don't see anybody else out there. I'm not a theory guy, but I would assume that all the control circuitry is still okay, but the "power amp" in the RF transciever section has blown.
I take the pragmatic approach. I have a laptop with builtin Ethernet NIC, and I have add-in PCMCIA cards for 802.11a, b, and g. Well, the g is USB, but you get my point.
If I take my laptop to your network, and I can connect but you can't, I tell you "I'm a trained, certified, and experienced professional network geek, and your wireless card has failed. You need a new one." And charge you for my visit.
Certainly, it's possible for your ethernet port to work, while the wireless side doesn't, in the same card. They are two completely separate sets of circuitry. They just happen to share a package.
Why don't you take your card to another known-working WLAN, and see if you can "see" their WRouter?
Also, as mentioned before, "g" is an improved version of "b". From the factory, your WRouter should accept both, but the "b" side may have failed, or it may have been turned off. Don't blame your card until you KNOW that the router is okay. They fail too.