If you broke any part of the home button, you must take it to Apple in order for you to have Touch ID and physical home button functionality back. The home button is "married" to the logic board, therefore there is no way to replace the button and expect to have any functionality.
Hello, I would recommend a battery replacement to start as batteries are relatively inexpensive. I had a similar problem to an HP Pavilion G7 and a battery replacement fixed the problem. Let me know if you need help! ~JS
Hello, This could be an issue with the cable that connects the screen the Logic Board. To clarify, do the colored lines appear then disappear after a period of time, or are they on all the time? Also, to better assist you, could you please provide me the model number if the iPod? Thanks!!
This same thing happened to me. The software version 10.10.5 will, over time, cause the FaceTime camera not to work. I simply updated my computer then I had no further issues. Let me know if this helps. If you are past 10.10.5 (Yosemite) please let me know.