Welcome to iMore! Does the phone make ANY sound, like music, message alerts, etc.? If so it's probably a software issue. I recommend going to Settings > General > Reset > Reset All Settings and seeing if that fixes your problem. If it doesn't then try restoring as new, preferably through iTunes. This article should help: http://m.imore.com/restore-iphone-ipad-itunes
If you're still having problems then it's probably hardware related and you should contact the seller.