Here are a few possible reasons:
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If you can't connect to youtube that means you are not in a wi-fi area. you need wi-fi to connect to stuff like tht
^^ that's not all... if you are connected to any wi-fi and it still wont let you connect its something with the router.
If its just saying youtube not available its something with safari or the youtube app (which is normally the one with the problems) all you have to do is reset it or go on youtube from which ever one is working.
Make sure the ipod touch is connected to your Wifi first.
Because the firmware has a problem and to that just restore the iPod and if that doesn't help restore all settings which won't affect apps or jailbreak ;)
If you could have YouTube videos in a format that iPod touch will play and were able to sync the videos to iPod Touch there would be no problem