The only time I ever found that type of powdery stuff was when I discovered that water had been leaking from around the basement's wash basin from the pipe coming out of the wall. It was a slow leak, but we have very hard water here in the mid-west, and the white stuff was the dried minerals and lime from each time the water dried up on the baseboard. I washed it all off with vinegar, and then had to have a plumber come in (and hope that won't be the case here!). I would double check any water pipes in the area.
