So I pulled the fridge out from its nook and saw that the plastic tube that feeds the icemaker had been pulled out of the little fixture through which the water then disappears into the machine, up toward the top of the unit, in back.

But even though I plugged it in, water did not start flowing into the ice maker. I unplugged the unit, replugged it. Nothing flowing. I even pulled the little tube back out and gave it a little suck, siphon-style! But that did not persuade any water to come up.

Is it possible that it only sends water at some point in its cycle, and until it hits that point in the cycle, water won't get pushed up into the freezer?

Or is there some sort of pump unit inside the icemaker itself that burned itself out because no water was feeding it? (That seems hard to believe -- isn't there just one pump in these machines, and it pushes water up from the base?)

Thanks for your thoughts