Acer Aspire One Laptop Makes Grinding Noise Only When I Play Music/Video?

This sounds strange in that you're saying it make a noise while watching youtube videos
so I think it will metal your cooling fan possibly full of dust and fluff (do you have a pet?) and with the CPU working harder to refresh the screen / transfer the movie file and sound file / check windows systems run background programs it is getting quite calorific so the fan works very hard to do so and if it is out od balance slightly then even more noise
With your music it is much the same in driving the HD to find the files and then process them to the sound card.
Have the cooling system cleaned first then think on other more expensive things.