My main PC (witch I'm sitting in front of now) runs Win7 Pro and it has no problem running YouTube on Chrome - IExx is a different matter (and one of the reasons I started using Chrome), where some will run and a lot of others NOT. IExx is not supported by a lot of homepages now, but I keep it for now as a few useful sites will not be shown in Chrome as it is sure they are Dangerous (and some are - so be careful with IExx).
I will not exclude that you have other issues here --> so start with making sure Windows is updated with ALL the latest safety updates (and drivers) from Microsoft.
If you have Adobe Flash installed - you might also have problems, as support ends this year -> most stuf using Flash will stop working. Since a lot of older videos on Youtube are using Flash ....?...?