If you're able to access your Nook Colors Settings, you can find the MAC address. I believe it's on the second page of Settings. Though it's been awhile since I used a Nook Color.
If you are looking at a registration screen, I believe you can skip that, though that may have changed in an update. If you are unable to get to the settings page without registering, I would suggest taking the Nook to a place which provides free WiFi.
Once you have the MAC address you can have the technically inclined household member add it to the routers MAC filter list.
You may want to test the Nook Color on an open WiFi connection, just to ensure that the WiFi is indeed still working. I've yet to see a Nook Color that had broken WiFi, but as with everything there is always a first time.
Any router with MAC filtering has a way to edit the list (warning: my routers default to BLOCK specified MAC entries, I have to make sure I set it to ALLOW only specified).
WEP using only 40 bits of key? That's rather weak security (I used to run 104 bits -- 26 hex) before changing over to WPA2 Personal -- mainly as I'm not using the older WEP-only devices.
Thanks to everyone for your help. Just as suddenly as the problem appeared, it went away. The most recent reply suggested rebooting the router. It turns out that the technically-inclined person in this household had already thought of that, but it didn't work at first.
I think that there was just slow response from the router, and the Nook may have timed out.
Thanks for sharing what worked. It'll help other people.
It's impressive that so many problems get fixed by rebooting the router/PC/laptop/Tablet/phone.