iPod turns on only when Connected. Help

Hi. I have an iPod Classic A1136. It was working fine until one day I tried switching it on from sleep mode and it didn't turn on.

I have the device fully charged.

I tried to connect it PC or a wall socket to see if it's not "dead" and it did turn on.

Now I have tried to reset the iPod restore the iPod from within iTunes but still the problem persists which is that it turns on only when connected for charging or when connected to PC (iTunes)

Could any one explain the problem and a solution for the same.

Thanks in advance