Are you using the YouTube app or the mobile version of YouTube, which can be found on http://m.youtube.com?
It could be that you are not on mobile data, and that's why you can't connect to YouTube itself. Try to make sure you have a proper connection to the Internet and see if you can view YouTube then.
In case you are trying to view videos that you have loaded on the phone itself, just go to Gallery and you'll find them all there. To view them on YouTube, you would need to create a YouTube account first, sign in, and upload your videos to the site.
Does that help? Let me know.