What have you got Settings > General > Use Side Switch To set to ? If the switch on the side is set to control rotation lock then you control notification mute by the left-hand end of the taskbar : http://support.apple.com/kb/HT4085
Are you sure that you have no sound in the Music App or in YouTube? None at all. If you do have sound in those - you probably have system sounds muted and there is another way to control them beside the side switch.
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 task bar. Double tap the home button and in the task bar at the bottom, swipe all the way to the right. The speaker icon is all the way to the left. Tap on it and system sounds will return.
If you have the side switch set to mute system sounds, then the screen lock rotation can be accessed via the task bar in the same manner as described above.
This support article from Apple explains how the side switch works.
You don't use Bluetooth headphones do you? If you do, turn them off and turn off Bluetooth on the iPad as well.
If you were using plug in earphones, plug and unplug them a few times and see if the sound comes back.
The only other things that I can think of would be to restore your iPad and if that doesn't work, you could have a hardware problem and they determination would have to be made by Apple via a trip to an Apple Store Genius Bar.
I would make an appointment. That way you do not have to wait in some long line.
If it is a hardware issue and the iPad is under warranty they will replace it - assuming that the hardware problem was not caused by accidental damage - like you dropping the device. It looks like you have the original iPad so the warrany might be up unless you bought the Apple Care.
They also offer out of warranty replacement iPads for a price of $249.00 in believe. You can look at this for more information.
I've had this a few times on my latest generation ipad. No sound in any application, or even system sounds. To fix it I hold down the power button until it says slide to power off, then power off, reboot it and all is fine. I do not know what is causing this problem but it must be a software bug in the IOS. I have the latest IOS6 and I do believe it did this before the upgrade as well. Very definitely troublesome since I use my ipad as an alarm clock. This morning I woke up 5 minutes later with it "beeping" only no sound so I didn't wake up.
Yesterday when I tried to watch TV CatchUp no sound came out of my iPad 3 using iOS 6.
I've tried every possible thing, I even reset it to the factory settings, but nothing.
I got the feeling it has something to do with iOS 6.
The odd thing is that when I try to set up ring tone it works, using headphones also works, but nothing else.
It's very frustrating!
First: I am extremely tired of people pointing me to the side-switch instructions. Useless.
Currently, my wife's iPad2 has pretty much no sound unless the headphones are plugged in. To be quite frank, if it comes down to "plugging and unplugging the headphones" and "seeing if that works", then Apple has a real problem. Also, if anyone suggests that this is a hardware problem, I will lose it ... there were no problems before the ios6 update ... if Apple broke her iPad, then Apple better fix it ... she used it heavily and loved it ... not so much now, and the upgrade did nothing but make it into a silent semi-brick.
I have nine Apple computers, 3 iPads, and 3 iPod touches ... I am a GREAT customer. This is the worst thing I have seen from Apple since I started buying their products about 15 years ago. Is this post-Jobs Apple? Well, I may be looking elsewhere.
I don't want tricks that "might work". I want an update that doesn't break my iPad.
FIX THIS! Put your billions to work and make this right.
OK: HERES THE SOLUTION TO NOT HEARING YOUR ALARM GO OFF ON YOUR IPAD IN IOS 6:
Had the same problem with an alarm I set. All I got was a notification on my screen that read "Alarm". Not very helpful when you're asleep. Here's what I discovered. You actually have to toggle the volume up when you're setting the alarm. The volume of the alarm is not based on the main volume, but adheres to the specific volume value you set when you're setting the alarm. Here are the steps.
Go to the Alarm tab on the on Clock App.
Hit the + button to set a new alarm.
Set the time you want to wake up.
Then select the ringtone sound. (It's normally Marimba by defaut)
So hit the > button next to the ring tone next ot Marimba and select another ringtone.
It will play an example of that ringtone.
At that moment you want to hit the physical + volume button on the ipad and you'll hear the volume of the alarm go up.
Keep raising the volume to the level you think will wake you up.
Save the alarm.
Now when your alarm goes off in the morning you'll actually wake up.
I know. It's totally unitiutive. Apple needs to fix it.