Is it all videos? Or just skating videos?
There are several possible reasons:
Does the startup chime sound? Can you play something from your Itunes? If these work, then your problem is not with the machine itself. If they don't play, these two things may help.
1. I'm not an Apple user, but you may have hit whatever they use for the mute button. Hitting the raise the volume button should turn it up. Or maybe hitting the mute button a second time. Apple is all too fond of toggles for my taste-the Apple assumption is that two wrongs make a right-hit mute on accident solution hit mute again ??? So try it.
2. The mute button could be stuck in some way. Here's what Apple customer help suggested:
http://www.justanswer.com/mac-computers/1h5ns-mute-function-stuck-imac-press-mute-button.html
Youtube has its own little peculiarities. If you can play something in Itunes successfully, try the next two:
3. Inside youtube, the last setting you had for sound was "mute". The next one you play will be muted. On the bar under the youtube video, there is a picture of a little speaker. Click it to turn the sound volume on.
4. Possibly Google is messing with you. One of the things that Google does to enforce music copyright on videos is to turn the sound off on the video. This happens often with skating videos. Try playing the recommended video at the youtube front page.
If you can't get Itunes to play
5. If you plug earphones into the computer, can you hear the sound on youtube? If so, try plugging them in and out several times. According to this thread, it may work.
Here's a thread discussing a similar problem
https://discussions.apple.com/thread/1736638?start=90&tstart=0
6. If none of the above work, your new Apple is under warrantee. Your new Apple is broken. They are rumored to have good customer service. This is why you pay the high prices. Take it back to the store. Tell them everything you tried. It may help them get it fixed.