Please update your plugins to the latest version. Check to make sure you are up to date:

• https://www.mozilla.org/en-US/plugincheck/

If you see any issues also see:

• Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems

This 'not h264 or webm' is a flag where I would suggest making sure that h264 is enabled or installed to support that codec (see attached images)

Thank you for your answer. It is not a problem with extensions (I tried safe mode, new profile, selective uninstallations etc.), nor with plugins (selective uninstallations). The OpenH264 Plugin is installed and activated (about:config tells me *lastUpdate = 1442537200, which is different to your value, but I guess this only means I have a newer update installed?). I also checked for codecs on my computer with the result that I have all the latest versions.

The detection code for MP4 doesn't work for me as well as it checks for a specific codec (avc1.42E01E).

• https://firefox-session-restore.herokuapp.com/

try {
  if ( bool = !!elem.canPlayType ) {
    bool      = new Boolean(bool);
    bool.ogg  = elem.canPlayType('video/ogg; codecs="theora"')      .replace(/^no$/,'');

// Without QuickTime, this value will be `undefined`. github.com/Modernizr/Modernizr/issues/546
bool.h264 = elem.canPlayType('video/mp4; codecs="avc1.42E01E"') .replace(/^no$/,'');

bool.webm = elem.canPlayType('video/webm; codecs="vp8, vorbis"').replace(/^no$/,'');
    }

UPDATE: After updating to Firefox 41 the browser no longer crashes when I close it. However, problems with media files are still the same.

Question: what is the proper configuration for Firefox --> Preferences --> Applications? I wonder if I should change everything back to default since I tried several things there to make media files work.

FYI: On my last computer media files didn't work in Firefox, even the new YouTube HTML5 player. I tried everything to fix it, without any luck. That lasted over a year while for some time I also experienced the crash issue at closing of the browser (that issue disappeared suddenly without doing something, but also no effect on media files). Suddenly, about 2-3 months ago, everything worked! I was able to play any file. I thought ok, on my new computer it should work considering it even works now on my cramped old machine. But now I have the exact same problem again! It is really getting on my nerves. Is Firefox not able to finally make HTML5 work without problems? Internet Explorer and Edge work totally fine but I definitely refuse to switch to those browsers only because Firefox can't play certain files.

To conclude: Probably not a problem with plugins, most probably not a problem with add-ons, definitely not a problem with computer or OS or hardware and especially graphics card, probably not a problem with programs such as antivirus and firewall since I changed that on the new computer, probably not a problem with preferences because a) it worked on the old computer b) it also does not work with a new profile or new installation, definitely not a problem with the server since I experienced the issue at several different sites over a few months. I can only guess it is some weird interaction between several things which happens to be the same on my two computers. First, I thought it would be a problem with preferences since I backed up my old profile and installed it on the new computer but a) it worked on my old computer b) new profile etc. didn't help anything

More FYI: The player normally shows up but when I check network analysis the file is not loaded (0 KB) and the player is either black or has an error message like "mime type not supported". I also checked for wrong or old codecs on my computer and I have everything in the newest version etc. What's kinda strange: If I download a video, let's say a .wav file and I open it with Firefox, it can be played! But not when I want to play it directly from the website. So, the problem must be somewhere in the transmission of the source information to the browser, I guess?

Holy f*ing sh*t!

I actually managed to solve the problem!!! https://www.youtube.com/watch?v=9N0OHdRFcJA

All I had to do was to start Firefox using administrator rights. So simple, yet I haven't thought about that! Why have I never tried that before? I managed to solve a lot of problems that way but never thought about the Firefox issue could also be related to it.

Anyway, thanks to everyone who responded and to everyone who had to read all my rants in this thread!

Solution: Start your Firefox using administrator rights