Guys,
I was only relating what had happened here with my computer at the time.
I can view videos now on YouTube fine, as wasn't the case the other night.
I even tried closing Firefox and then opening it again, but I still ended up with the same screen when I clicked on my YouTube bookmark.
I have a tonne of "Favourites" on YouTube that I like watching, I might just have to bite the bullet and sign up with a Google account.