The funny thing is that the guy at the Genius Bar was not surprised in the slightest that the machine was dead.
Also, when I called today they said I'll get a call either Monday or Tuesday with the return shipping info. The guy in the store said that they can ship me a new machine as soon as they have one and they have confirmation that FedEx received my machine. I wonder if he is right?
That's how it worked for me. Thursday evening, when FedEx scanned the original machine I was sending back - I saw the process begin on the replacement.