YouTube uses Adobe Flash to play the videos, and it's possible your Firefox Flash is corrupted.
I would visit the Adobe web site to download and install their Flash removal tool, use that, reboot the system, (to make sure any remnants are removed), then back to Adobe to download and install Flash once again.
Whenever I try to load a youtube page, there is 50/50 chance that the page willl hang/freeze.
And sometimes when I try to load a video, the video just won't play. Chrome and IE run just fine on youtube.