Did you disable stylesheets? That sort of thing happens if stylesheets are not used. Check the View > Use Style menu and see if "None" is selected or "Basic Page Style" or "Default Style". You do not want to select "None".

If you have Avast then try to disable HTTPS scanning in Avast Web Shield.

• http://www.ghacks.net/2014/10/31/avasts-https-scanning-interferes-with-firefox-and-other-programs/
• https://forum.avast.com/index.php?topic=176073.0

You can check the Net log and the Network log in the Web Console (Firefox/Tools > Web Developer) to see if content fails to load or possibly is blocked (file size is zero).

• https://developer.mozilla.org/Tools/Network_Monitor

Use Ctrl+F5 or Ctrl+Shift+R to reload the page and bypass the cache to generate a fresh log.

YouTube style sheets are loaded from a second server. Can you access the style sheet directly using this link:

https://s.ytimg.com/yts/cssbin/www-core-2x-vfl74wlma.css

It should open a tab listing a "wall of text" (style rules written without spaces or line breaks), starting:

body{line-height:1;text-align:left;text-align:start}menu

If you get an error or if Firefox won't display the page but forces a download, that may help explain why YT appears unstyled.