So wouldn't you know it, after doing the factory reinstall and then grabbing all the latest Windows Updates... the Wireless networking started doing the exact same thing as before! Gah! But, this time I didn't have system restore disabled, and so I was able to roll back to before grabbing all the updates. After a restore and a reboot, the wireless was working again, so obviously one of the updates broke the functionality of the wireless.
At that point, I decided to try grabbing all of the updates with a couple exceptions: I left off .NET 4 (it's new and I encountered an issue on a different PC recently), and I didn't grab the optional updates. So really I installed about 98% of the available Windows Updates. Rebooted and everything still worked, so then I tried the optional updates as well as .NET 4. I was able to determine that the actual culprit was a Realtek network driver, but the catch is it was theirwired network driver, and it was breaking the wireless networking functionality. Okay, "breaking" isn't entirely accurate, since you could still get it to work, but anyway I left off that driver and now the laptop is up to date and running happily. Interesting to note that the wired Realtek driver was just published in the last week or two, which is why I didn't encounter the problem before.