On/off button stuck fast.

Yes, it can. There is a tiny spring on the power button (the volume and power button are all one piece, meaning you'll have to replace both) that is possibly broken. I would try to replace the on/off/volume buttons, and see if that solves the problem. As for parts, at last checked, I have found the buttons part listed for $4. Just go onto eBay and type in iPod 6th generation nano power button with tools. You will have to reuse the button pieces themselves, though. All they give you is the part itself. From my research, I would conclude that it would cost $5-$20, though I wouldn't recommend anything shipping from Hong Kong or the Philippines, just for quality and shipping reasons. Don't forget to find a guide online of how to replace it. Hope this helps!