So apparently a small number of Wiis have a firmware issue in which the first update burns the system out so it can no longer update or connect to the internet. I finally hit the small odds on something. Took three days to reach Nintendo (storms in Redmond so the techs were out), but at least once I reached them everything was smooth. New box being sent out, then I can ship the old one back. Lose my saves though, goodbye to 11 hours on Twilight Princess and 8+ on Rampage (the update that burns out the system is the one that lets you transfer saves to SD card...).
On the whole it could be worse, more amused and annoyed than enraged.