It would be odd for a PC to have never worked but I've see it blow up after use of driver updaters and registry cleaners. My recurring fix is to get the drivers from the maker and try again with another USER account.
However there are some sites where th embedded YouTube will NEVER EVER go full screen. That scenario is a lost cause. But you can usually watch it on YouTube.com directly and it works there.
As to IE, it's a minefield. I'd try Chrome and Firefox first.
How can I troubleshoot why the full screen mode in youtube won't work. I posted a search question on the website, and turned up one scenario; apparently it is a problem with settings not working in Chrome. But that wouldn't be the issue with my question since we use IE. Its a WIN 7 gateway pc. It worked fine before. It will be great to figure it out. Oh yes; BTW I did check in programs and flashplayer is up-to-date. I thought that might be an issue. Maybe it isn't the computer? Thanks for any help.