Shit on fire.
It wasn't the Airport Card. It was the socket on the logic board that the Airport Card connects to. I took the computer into the shop 2last Thursday (08Jun), and they were able to diagnose the problem over the weekend. Then they had to convince Apple that they were right. Finally, last Friday (16Jun), the logic board replacement was authorized. It is expected to arrive at the shop this Wednesday. So hopefully my MBP will be back home by next weekend.
Apple may make really good computers, and a nice OS to go with it. But when they fuck up, they fuck up good. And they're nice and slow at getting the problem resolved. If it was my company, I would have handed me a brand new MBP and said "No hard feelings, we value you as a customer". Fix the busted computer later, while the customer is telling his friends how awesome Apple support is. Unfortunately for their PR, this is not how they handled it. I still love Macs, but I am kinda unimpressed by the way this issue has been handled so far. I've had the computer for almost a month, and it has only been useable for like a week!