Have you checked the following
1. Touch the Home Key > Menu Key > System settings > Sound.
2. Touch Phone ringtone
3. Scroll through the ringtone list and select the ringtone you want to use.
4. Touch OK to save.
Also check the following
1. Touch the Home Key > Menu Key > System settings > Sound >
2. Adjust the volume for the ringtone volume
3. Touch OK to save.
Also check that you haven't enabled silent mode with vibrate
Touch the Home Key > Menu Key > System settings > Sound >
Silent mode, and touch Vibrate or Mute.
What you need to do now is prove whether you have a OS or software problem.
My suggestion is to do the following:
1. Ensure the phone's battery is fully charged.
2. Backup the phone using the backup feature.
3. Do a factory restore using the factory restore feature, - this will erase all your downloaded apps and user data and restore your phone to a factory default condition. Like it was when you first bought it.
If the ringtones still don't work after this, it is a OS problem. Check the warranty period of the phone and if still valid contact the manufacturer's customer service section regarding a warranty repair / replacement.
If it works then one of your downloaded apps may have caused the problem, When you restore your phone to what it was, using your backup, if it fails again it is one of the downloaded apps, if not it may have been a setting that wasn't restoring properly and has now cleared..