Google deploys YT cache servers within ISP networks to help reduce traffic across the Internet core. My guess would be that your local cache server is having issues. Try to access a really unpopular video, like say...
https://www.youtube.com/watch?v=LB6oPr5Z36E
Since cache servers only cache the popular videos, this one would be fetched from YT's own infrastructure. If this video loads fine but your popular videos don't, the issue is probably on your ISP's side and you could call them to complain. xd
Ashikoki 2 lewd.