So it is still running 6.6.1?
I think in that version YouTube was removed because it was not compatible with the current iteration of YouTube. Just like on one of the original iPod touch with Apple's YouTube player, it won't work.
You need to upgrade to 7.5.
7.6.1 is the one that everyone is having problems with, not 7.5.
You need to upgrade to it with the downloaded 7.5 binary which I will not link to here. You can find it by searching for it on TidBITS in the comments regarding to the article that deals with 7.6. Scroll down in the comments and you will find a user that posted a link that works. Don't use the one that the author of the article posted.
But yeah, you're not going to get a working YouTube on 6.6.1.