New iPod Touch with grayed-out "No Wi-Fi" text in Settings

Question

Just got a 16GB iPod Touch as a refurb. from Apple Store. I install iTunes, hook it up to my computer, follow all the instructions, and then after it's charged, disconnect it to begin using it.
First thing I do: try to set up the wi-fi. Only problem: I go into Settings and at the top, where it says "Wi-Fi" it is grayed out, and says "No Wi-Fi" next to it. In the About section, it says "N/A" for MAC address.
I have turned the unit off and on, performed a soft reset, a full restore through iTunes, and even paid the $4.95 to upgrade the OS to 3.1.2, thinking that version 2.x might be the problem.
Still... no Wi-Fi. According to Apple's site, refurbs are supposed to be fully tested and brought back up to factory spec before being shipped out. What hhappened to THIS unit? How'd it make it from China to my porch without anyone at Apple ever turning it on to see if the wireless chip in it even works?
Now I've got to go through the hassle and delay of exchanging it and waiting for the replacement to come in the mail from half a world away. Here's an idea, Apple... sell refurbished stuff that works with the guarantee that if it doesn't work or if it's defective, the customer is guaranteed a brand new unit as a replacement. Maybe that will light the fire under the techs to make sure they don't send out broken equipment as "Apple Certified."

Answer 1

I completed the instructions in the linked knowledge base article. It did not fix the problem. Apple has agreed to replace the unit after I ship it back to them. I will now have to wait another week before another refurbished unit arrives from half-way around the world...
I think my problem with this whole thing is that Apple specifically touts the fact that refurbished units sold through their online store are extensively tested and will work like a brand new unit. Obviously nobody even turned this unit on and went to the basic "About" screen in Settings to see if wireless was working. They would have caught the problem right away.
This is a check that should have taken 5 seconds for a technician to perform and would have saved me the disappointment of having the first iPod I've ever owned be a lemon... and saved me another week of waiting for a gizmo that I had expected to be using already. Don't sell Apple Certified refurbished stuff unless you're going to actually turn it on and make sure it works!
My other complaint... the rubber seal between screen and metal case is bulging out at two corners. It looks shoddy and cheap. I don't know who worked on this particular unit, or if this is par for the course with Apple. If the next one looks shoddy too, or has any problems, it will be my last time trying to get an Apple iPod. I got refurbished since I don't have much money - and I just can't justify spending the amount they charge for a new one. One more try Apple...