Try turning on the Assistive Touch.
While this won’t actually fix your problem it gives a temporary solution that allows you to adjust the volume of your iPhone. You simply go to
Settings>General>Accessibility and turn on Assistive Touch.
If you try to tap the volume buttons they may work after a while. What I believe you may have to do is re-seat the cables and try putting the phone back together. It is possible one of the cables may have been damaged during replacement or it could have been a defective part if everything went smooth. Not uncommon with some places but I wouldn’t rule out damage either.