There are two different versions of Flash for Windows, the ActiveX version for IE and the Plugin version used by Firefox and most other browsers.

1.Download the Flash Plugin version setup file from here:
Adobe Flash - 32-bit Plugin version.
Save it to your Desktop.

2. Close Firefox using File > Exit
then check the Task Manager > Processes tab to make sure firefox.exe is closed,
{XP: Ctrl+Alt+Del, Vista: Shift+Ctrl+ESC = Processes tab}

3. Then run the Flash setup file from your Desktop.

4. Start Firefox and test your installation here: https://www.adobe.com/software/flash/about/

• On Vista and Windows 7 you may need to run the plugin installer as Administrator by starting the installer via the right-click context menu if you do not get an UAC prompt to ask for permission to continue (i.e nothing seems to happen).
  

See this:
http://vistasupport.mvps.org/run_as_administrator.htm

I've tried every steps on the instruction above and enabled all plugins in FireFox but it still didn't work!! I open Internet explorer and tried to play the same video, it's working fine. What I have to do next to solve this problem?

This is the list of Installed Plugins from More System Details in your original posting.
Adobe Flash is missing - it's either disabled or not installed. Shockwave for Director is a different program.

   * Adobe Shockwave for Director Netscape plug-in, version 11.6.3.633
   * DivX Plus Web Player version 2.1.3.529
   * Google Update
   * iTunes Detector Plug-in
   * DivX VOD Helper Plug-in
   * The QuickTime Plugin allows you to view a wide variety of multimedia content in Web pages. For more information, visit the QuickTime Web site.
   * Version 1.9.2.0
   * Google Talk Plugin Video Accelerator version:0.1.43.5
   * Garmin Communicator Plug-In 2.9.2.0
   * Next Generation Java Plug-in 1.6.0_19 for Mozilla browsers
   * Photodex Presenter Plugin 4,10,0,2712
   * ShiVa3D Plugin 1,8,1,1 for 3D real-time applications made with ShiVa Editor.
   * npmnqmp 989898989877
   * 6.0.12.448
   * RealPlayer(tm) LiveConnect-Enabled Plug-In
   * Office Live Update v1.3 

Sure it may work in IE and not in Firefox, if you have the ActiveX version of Flash installed and don't have the Plugin version of Flash installed. Do you see both versions listed in the Control Panel > Add /Remove Programs?

I had both Adobe Flash Player 11ActiveX and Adobe Flash Player 11 plugin when I open add\remove program in control panel.

Does Shockwave Flash 11.x.xxx.xx appear in Plugins in the Add-ons Manager?
Is it (disabled) there?

http://kb.adobe.com/selfservice/viewContent.do?externalId=tn_19166&sliceId=2

No!! I was enabled. Should I try uninstall FF and reinstall it??

That screenshot shows all those plugins as being (disabled) and "greyed-out" - click the Enable button on the right-side.

Oh !! So that was the problem. Thanks for your help!!!