Clear the cache and the cookies from sites that cause problems.

"Clear the Cache":

• Tools > Options > Advanced > Network > Offline Storage (Cache): "Clear Now"

"Remove Cookies" from sites causing problems:

• Tools > Options > Privacy > Cookies: "Show Cookies"

Start Firefox in Use Troubleshoot Mode in Firefox to check if one of the extensions or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox (Tools) > Add-ons > Appearance/Themes).

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.com/kb/Safe+Mode

The latest Adobe Flash plugin adds a 64-bit player as well as the standard 32-bit player. Youtube seems to set a cookie that conflicts with the 64-bit version and therefore causes you to see a black screen when trying to play videos. All you will need to do is go to the Firefox menu on the top left, then go to History -> Clear Recent History. From there, make sure both Cookies and Cache are checkmarked (feel free to uncheck everything else) and then make sure that the "Time range to clear" setting has "Everything" selected. After that, click the Clear Now button and you're done. You should now be able to play Youtube (and presumably) other videos again.