Even though you said that you checked settings and you reset the iPad, I don't know what settings you checked or how you "reset" the iPad so if you tried one of these four suggestions already, my apologies.
1. If you have no sound at all, even in the Music App, try rebooting the iPad.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
2. Reset all settings. Settings>General>Reset>Reset all settings. No data will be lost but you will have to enter all of the device settings again.
3. If you lost sounds for keyboard clicks, games or other apps, email notifications and other notifications, system sounds may have been muted.
System sounds can be muted and controlled two different ways. The screen lock rotation can be controlled in the same manner as well.
Settings>General>Use Side Switch to: Mute System sounds. If this option is selected, the switch on the side of the iPad above the volume rocker will mute system sounds.
If you choose Lock Screen Rotation, then the switch locks the screen. If the screen is locked, you will see a lock icon in the upper right corner next to the battery indicator gauge.
If you have the side switch set to lock screen rotation then the system sound control is in the control center. Swipe up from the bottom of the screen to get to control center . Tap on the bell icon and system sounds will return.
If you have the side switch set to mute system sounds, then the screen lock can be accessed in the same manner as described above.
This support article from Apple explains how the side switch works.
4. If you still have no sound at all - except when using headphones ....try cleaning the dock connector opening of the iPad with a soft brush and just a little bit of rubbing alcohol.