A battery replacement shouldn't do that. Unless someone disconnected something.
Have you gone into the phone's "Settings" and checked to make sure the sounds are indeed set as on and also that all the volumes are up where you want them? It is possible when whoever it was changed the battery that they turned them off.
If it persists after that, try starting up the phone in "Safe Mode" and see if you get sounds in there. If you do, then there is something on the device stopping them (bad app, virus, etc.). However, if they still don't work in "Safe Mode" then I would take the phone back to who ever it was that did the battery replacing ad get them to fix whatever they damaged.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.