Do you have that problem when running in the Firefox SafeMode?
http://support.mozilla.com/en-US/kb/Safe+Mode
Don't select anything right now, just use "Continue in SafeMode."

When in Safe Mode...

• The status of plug-ins is not affected.
• Custom preferences are not affected.
• All extensions are disabled.
• The default theme is used, without a persona.
• userChrome.css and userContent.css are ignored.
• The default toolbar layout is used.
• The JIT Javascript compiler is disabled.
• Hardware acceleration is disabled.

If not, see this:
https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fi...

Have tried all the things you listed plus everything under Firefox help guide to no avail so far. The problem persists in safe mode and I have reset Firefox multiple times with no results.

Do you have a content filter or Firewall perhaps blocking assets from yahoo?

No have not changed any settings in browser and have tried with firewall disabled with no success either.

I have the same problem, and I have tried all the troubleshooting and checked other support articles and users with similar problems, but still no luck. (Firefox 23.0.1, Windows 8, on a new sony i7 laptop)

All plugins are up to date. Internet Explorer plays all these files without any problem, so I know it has to be Firefox issue or bug.

For example, I cannot play this video on Firefox, but it plays on IE:

http://autos.yahoo.com/blogs/open-road/top-five-sleeper-cars-video-205832307.html?vp=1

Problem solved! I downloaded and installed Firefox 24.0 Beta. Apparently Mozilla programming team made all the right changes in the new release. Now all videos starting working on Yahoo and BBC.

Link: http://www.mozilla.org/en-US/firefox/channel/#beta