Even so, I decided to check teh Google for suggestions and similar experiences. On the Nintendo support boards, I found the following post in response to another gamer who'd experienced the same problem.
Did you have any power issues recently in your area?
If so, there might be a problem with the surge protector in your AC adapter.
Unplug it from the Wii and the wall. Also, separate both halves of it. Let it sit for 30 minutes to an hour. Plug it back in, making sure all connections are correct and strong (plugged in all the way).
Then, try to turn your Wii on.
If that doesn't fix your problem, try again on a different outlet.
If you cannot solve this issue, contact Nintendo for more help from an NOA representitive.
Try calling nintendo's support hotline, toll free:
Or using their online support:
Online support may not have the answer to what you need, in which case it will lead you to a webform E-Mail service to get personal help.
It worked! We were playing Okami an hour later with no data loss. It would suck to lose 30-40 hours of saved game play. I also found posts (on Gamespot, I think) that mention that Nintendo will send you a new AC adapter if need be and that their support line is very helpful. One poster even said that they'll even send you a new Wii in some cases. I'm not sure I believe that one, but the upshot is that Nintendo support obviously has a good rep.