We have water again! (And I don't mean puddling all over the utility room floor!)
Donald poked around some. Mom and Dad came over and looked and gave their in-put. Donald cut a hole in the drywall, and we found the source of the leak (in a tangle of water pipes).
Long story short, we ended up calling a plumber. We decided this was one of those times that getting a professional to look at the problem was worth what we might save trying to figure it out on our own.
(Do you see much difference? No, neither do I, really. The "after" is a little more organized, though.)
And so, in conclusion, dear Reader ;o), take a moment to appreciate your indoor plumbing and the fact that it is not presently leaking. And if you've never experienced a pipe leaking behind a wall, consider yourself very lucky.
It didn't cost an arm and a leg to fix the pipe (and some of the surrounding pipes), so that's good... On the other hand, the plumber said that our problems aren't really the fault of the original plumber (even though his work looks awfully messy to me... but I guess I'll withdraw my earlier wish to dropkick him). Instead, it's probably just our water. (Lovely. Maybe water that corrodes metal is actually super-duper healthy for people, though. There has to be some silver lining here, right?) He recommends putting a filter out by the pump, so we're going to look into that (and just hope that no other pipes go pop anytime soon). Also, we're going to leave an easy access panel over this area of the wall in case we ever have problems with any of these pipes in the future. (The silver lining here is that it's behind the washer and drier, so no-one will even know it's there.) No more guesswork as far as where those pipes are!