A long shot and I'm not quite sure if it's been covered here.
In Settings/General there is a setting called "Use Slide Switch To:"
You can select the slide switch so it controls either rotation lock or mute. If it's switched to "Lock Rotation", you need to make sure you haven't muted your speakers in the switcher bar.
To check this, go to Home screen and swipe up with 4 fingers. This obviously shows the apps bar. Now swipe the apps bar to the right (push it towards the right side of the screen) this reveals your iTunes player controls and on the far left is the Mute/Unmute button. make sure this is turned off. Slash across means muted.
Note that if you have your Slide Switch set to Mute/Unmute, then this apps bar button will switch the lock rotation feature.
Hope this helps, coz it sounds like the "problem" I had with my new iPad, and stumbled across my solution quite by accident...!