I had a similar problem with Mint 13.
My issue was the audio source.
In System->Preferences->Sound Preferences --- Hardware Tab
I have two audio devices:
1) Built in audio
2) RS880 HDMI
I tried both until "test speakers" produced audio.
Then go to the output tab.
The same 2 audio devices were there, but the incorrect one was selected.
As soon as I changed it to the one that worked for the speaker test, the audio from youtube worked and it played at normal speed.
I had a similar problem with Mint 13. >Preferences- >Sound Preferences --- Hardware Tab
My issue was the audio source.
In System-
I have two audio devices:
1) Built in audio
2) RS880 HDMI
I tried both until "test speakers" produced audio.
Then go to the output tab.
The same 2 audio devices were there, but the incorrect one was selected.
As soon as I changed it to the one that worked for the speaker test, the audio from youtube worked and it played at normal speed.