Did you reset the iPad? Hold down on the sleep and home buttons at the same time until the Apple logo appears on the screen.
Do songs in the Music App work through the speaker on the iPad? If you can hear that sound, then system sounds are 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.