Make sure you are not blocking content.

Start Firefox in Safe Mode {web link} by holding down the <Shift> (Mac=Options) key, and then starting Firefox.

A small dialog should appear. Click Start In Safe Mode (not Refresh). Is the problem still there?

this enables the Youtube videos to start properly. but now all other facilities don't work anymore like LastPass (auto fill-in generated passwords), coockies, and several others. how to solve it?

It could be the work of one of your add-ons, or it could be Hardware Acceleration. How to disable Hardware Acceleration {web link}

Type about:addons<enter> in the address bar to open your Add-ons Manager. Hot key; <Control> (Mac=<Command>) <Shift> A)

In the Add-ons Manager, on the left, select Extensions. Disable a few add-ons, then Restart Firefox.

Some added toolbar and anti-virus add-ons are known to cause Firefox issues. Disable All Of them.

If the problem continues, disable some more (restarting FF). Continue until the problem is gone. After, you know what group is causing the issue. Re-enable the last group ONE AT A TIME (restarting FF) until the problem returns.

Once you think you found the problem, disable that and re-enable all the others, then restart again. Let us know who the suspect is, detective.

https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode

Safe Mode is a troubleshooting mode that temporarily turns off hardware acceleration, resets some settings, and disables add-ons (extensions and themes). If the problem goes away, that tells us one thing. If it does not, that tells us something else.

all right!!! the trouble maker is detected: it appears to be the YouTube Flash Player. whille all other extentions function properly, even when enabled simultaneously. It is mostly surprising that exactly this extention caused the problems whereas it was the least suspected!!! many thanks for your excellent advice.

YouTube no longer supports flash. remove that add-on and you should be set.