My sisters 1GB iPod Nano is stuck on the Apple Logo Screen and will not shut off or reset by holding the buttons down. It doesn't mount or open iTunes when plugged into a computer.
My friends iPod did this too, she had to let it run out of power then when she charged it, it worked fine. Have you held the centre button and either play or menu (forgot which one) down together for a few seconds?
Turned it on today after letting it die last night. Held the Center and Menu buttons until the screen lit up and then pressed Rewind which made it changed menus. It is now charging up and it has mounted on the Desktop.