Do you have any add ons installed? I installed "NoScript" in Firefox which blocks imbedded scripts on a given web page. I know if I do not allow scripts on youtube's site, it wont load videos. I'm running a Mac and rarely enable the built in firewall, so if you're running a PC, maybe the firewall settings are blocking youtube's videos from running/loading. Just my 2¢s Good luck.
+1 on clearing caches and histories. I know that there are certain age restrictions on youtube that if you do not register and provide a D.O.B., it won't load videos in your browser if they don't think you're over 18, are you registered w/youtube?
Again, just my personal experience, your results may vary.
Greg