Alright, never mind. It's going now. In my infinite wisdom and affinity to reset things when they're not working, I just turned off the power to my router, then turned it back on and ran another connection test from my Wii. Bing, working.
Just so I know though, would the reset have actually done anything to help (or anything potentially damaging), or was it just being bitchy and the reset had nothing to do with it?