Which Which

Me: "So we know that the laptop won't work wirelessly, because the desktop computer we're looking at, which is connected with an ethernet cable, isn't working."
Customer: "Well, yeah, I think the desktop computer won't work either."
Me: "So... there's another desktop pc?"
Customer: "No, just the one main computer."
Me: "Isn't the desktop the main computer?"
Customer: "Yes, I carry the laptop around from room to room."
Me: "So which one have we been working on all this time?  I thought it was the desktop."
Customer: "The laptop."
Me (biting tongue): "Well, let's take a look at the desktop then."
Customer: "This is the desktop."
Me: "The computer that we've been looking at: is it the desktop or the laptop."
Customer: "Yes, it is."
Me: "The desktop?"
Customer: "Yes, the laptop."