I don't know where you were checking in your settings, so I'll suggest what you could do, in case you didn't already look there.
In Settings - General - Use Side Switch to: did you choose "Mute" or "Lock Rotation"? If it's set to mute, toggle the side switch once or twice and see what happens.
Settings: did you by chance enable "Do Not Disturb"?
Also Settings: Sounds - Ringer and Alerts: is "Change with Buttons"enabled?
What else you could do:
Look at your connector and clean it. Do so very cautiously, with a soft brush.
Also try the usual fixes:
Restart your device: turn it off, wait for a few minutes, turn it on again.
Reset it: press and hold Home and Power button simultaneously until the Apple logo appears, then release both and let the iPad start on it's own.
Force close apps (some games mute sound on iPad, force closing might help find the app that's causing it):
iOS 6: double tap Home button or four/five finger swipe to reveal the multitask bar, then tap and hold an app icon until they start to wiggle, delete them.
iOS 7: same procedure to reveal multitask bar, then swipe thumbnails (above app icons) towards the top of the screen.