Seems like your iPad is acting as if it has no WiFi at all, unless the WiFi module was not even installed in the ipad during manufacturing - pretty rare but anything is possible with mass produced items. Have you tried doing a full restore? Other than these suggestions, get it exchanged as you have the visual proof wifi wont work.
His (I'm assumin OP is male) didn't, that's why it was replaced (see one post above yours).
I'm glad they helped you nout OP - I watched the video and it looked like the software recognised the fact that the hardware was unavailable.
Edit: To quote Terry Pratchet's Maskerade: 'And all those exclamation marks, you notice? Five? A sure sign of someone who wears his underpants on his head.'
Edit: To quote Terry Pratchet's Maskerade: 'And all those exclamation marks, you notice? Five? A sure sign of someone who wears his underpants on his head.'