iPod nano 6th gen (brand new) doesn't recognize when headphones are plugged in

I have a brand new iPod nano (6th gen), and it doesn't detect when headphones are plugged in. I have read that the problem can ocurr because the headphones are not correctly inserted (which is not the case.. i'm absolutely sure about this) or that the headphone jack has dust inside (which is also not the case, since it is brand new).

This is what happens:

When i play a song, and then press the sleep/wake button to turn off the display, the music stops. Or if i let the music play, it stops when the screen times out and turns off. These two things occur because the ipod "thinks" that there are no headphones inserted.

When i try to activate the FM radio, the radio won't start because it says that there is no radio signal (which occurs when no headphones are connected).

Needless to say, the microphone and volume controls of the iphone headset, don´t work at all (they even work on the ipod shuffle!).. and because of this, no voice recording for me!

It's a shame, because the FM radio is completely useless, and music playing only works by activating the "double click to play" option in the settings menu.. but it is somewhat cumbersome the process of "play music - turn off the screen - double click to resume playing" every time I select a song.

The headphone detection has only worked randomly when the ipod is connected to the computer, but i haven't been able to figure out under what conditions this occurs. I have read about this issue, and I only would like to know if this is a firmware bug of the 1.2 version. I tried unsuccesfully to downgrade the firmware to the 1.1 version (maybe because the ipod shipped with the 1.2 version).

I have also restored the device in itunes, with no luck.....

Thanks in advance for any useful answer!