Is the phone charging? Headphones jack is working? Answer this first.
Second, did you disconnect the lightning connector during the battery replacement? Did you nick something on the board, and/or did you pry at any time between the battery and the logic board, especially next to the charging port connector? Also tell us.
Third, as a quick troubleshoot, disconnect the screen, disconnect both the battery connector and the lightning (charging dock) connectors. Clean the charging dock connector on the board using a cotton swab and 90%+ isopropyl alcohol, then reseat gently and make sure everything is connected properly. Test the phone again, is the mic working? is the phone charging? Is the home button now working?