Clean out your cache, cookies, temporary folders, history etc. on your browsers (usually under "tools") then try again. If that doesn't help, download "spybot
search and destroy" type that in Google and have it updated, then scan your system completely there may be a malware or adware problem. Try going in YouTube after that. If that that doesn’t work, then check your internet connection speed, if you’re using wireless or wifi, try going closer to the router, or even try it with a cable connection for test purposes. If wired connection lets you watch on YouTube but wireless doesn't, then you have an obvious case. Then you should upgrade hardware relating to the internet wifi.
If all that doesn’t work, try downloading Internet explorer 7.0 and see it that works, after disabling all firewall settings.
If that doesn't work, then upgrade your RAM on your system. If your lappy has RAM id significantly less that 512MB, than that may be the problem.
I have tried to give you all possible solutions, there may be more, but that’s all I know. Explore your options.