iPod nano (4th gen) plays any song for 40 seconds, then stops

Strange behaviour from my 4th gen iPod nano:

1. When plugged into Logitech iPod dock, plays any song selected for 40 seconds, then stops. Hit play, it plays for another 40 seconds, then stops again. (Logitech iPod dock works fine with my wife's iPod nano.)

2. When plugged into the Pioneer car stereo, the car stereo reports that the iPod is in SET UP mode, which it never comes out of. (As above, car stereo has no problem with my wife's iPod.)

3. iPod nano is detected normally by iTunes and works normally when plugged into desktop computer.

4. iPod (and iTunes) software is up to date.

5. Resetting the iPod (Menu + Centre button hold) has no effect on either (1) or (2) above.

6. Help?

Steve