At the bottom right of your screen, can you see a speaker icon? If so click on it.
There you'll see two possible reasons why you can't hear audio.
1) Speaker button. If it has a little "no entry" sign next to it then your speakers are muted. Click it to un-mute
2) Volume control. If the slider is set near the narrow end then you have turned the volume down. Click and drag the slider up to increase the volume
If neither of those things are wrong, try re-booting the laptop.
Thanks for all your answers. Mr.c.'s got it working temporarily but have to do something to every video separately. It's the same on desk top and that has separate speakers.
Chances are that flash content is being blocked by a firewall or your router its self. Reboot your router and see if your desktop and laptop will play sound from youtube.
If you can play other 'music' without an issue then the problem is not server side nor is it your sound drivers.
The firewall idea is a little far fetched since you've tried two seperate machines. I'd like to know what jiggery pokery your OH did to get the videos to produce audio.
so would I, but it's working that's all that matters. Son-in law usually sorts out any major problems when he's not busy. Neither me or mr.c are any good with computers.