If neither of those have fixed the issue, you need to replace the connecting flex that connects the Ear Piece Speaker to the main board, follow this guide and see if it works for you Best of Luck Regards
If you attempt to restore it, the Touch iD fault might cause the phone to brick and bring up the Touch iD Failure error. My advise, open the phone again, make sure the connection for the Home Button is connected correctly, also check carefully that all the pins are somewhat straight and not bent. Next is to check the flex cable that connects the Home Button to the main board, make sure this is not damaged in any area (not ripped or torn). Did you replace the Touch iD / Home Button while replacing the screen?
Hi Ted You will need to follow the disassembly guide, once you have the iPhone motherboard removed, you will need to remove the Heat / Metal shields and clean underneath them, general I use 99% IPA, or Distilled water in a Sonic Bath, they work well. You may need a battery that has charge in it to test it after you complete this process, but cleaning it is very important. Unless you replace the whole motherboard with a new battery and display Best of luck Regards
You may have recieved an iPhone 5S battery rather than an iPhone 5C, the connectors are extremely similar but they are different. Purchase a battery from iFixit that way you know it is the correct battery, the only difference is the capacity of the battery iPhone 5C = 1510 mAh iPhone 5S = 1560 mAh Best of luck Regards