So my question What could have caused the * key on my numeric keypad to stop working in Windows 7? got deleted yesterday as too broad. I just voted to undelete it today, because I figured out the problem.
However if this seems like not a good question for the site, never mind. My answer is kind of like the related question where the person found that Texter software was intercepting some keys.
I followed the comment's suggestion to re-seat the key, but waited for the problem to happen again. That wasn't it.
In my case, it was another particular piece of software I'd not have suspected to intercept keystrokes, but it was. Going into options, I was able to un-map those keys.