iPod Nano 4th gen - screen flickers, won't turn on, isn't recognised by computer or iTunes.

My 4th gen iPod Nano has been playing up.

When I connect it to my computer or a dock, the screen flickers with the Apple logo. Once unplugged, it won't turn back on and the screen goes completely black. I tried to reset it numerous times (both connected and unplugged) but that didn't help at all.

I tried to see if I could fix it by restoring it and putting it in disk mode, but the iPod isn't recognise by any of the computers in my house and doesn't appear in either iTunes or 'My Computer' so that really doesn't help. I'm positive it's not an issue with my computer or USB cable because the other iPods in my house connect just fine.

Any idea on how to fix this?