Note to Self (and Google):
When your Wii hasn't been played in a few weeks and won't turn on, don't panic. It happened to me this evening when the girls decided out of the blue that they had to use the Wii. The little red "Standby" light wasn't on, it didn't respond to any button pushes, and it looked dead.
After a bit of Googling, I tried unplugging it, left it unplugged for about 5 minutes, and then plugged it back in. The light came on, everything booted up, and the girls are now happy campers. Crisis averted. hopefully this gets indexed and saves some other father from 45 minutes of "Why isn't it working, Dad? Can't you fix it, Dad?"