Try to rebuild the Windows icon cache.

1. Open the Task Manager (Shift+Ctrl+ESC)
2. In the Process tab, right-click on the Explorer.exe process and select End Process.
3. Open the file picker via "File > New Task (Run)" and click the Browse button.
4. Type or Paste %USERPROFILE%\AppData\Local in the File name field (AppData is a hidden folder).
5. Select the IconCache.db file and use "Delete" in the right-click context menu to delete the file.
6. After the IconCache.db file has been deleted, start a new explorer.exe process via "File > New Task" to get the desktop and Taskbar back.

The IconCache.db file is a hidden file, so make sure that you can see hidden files.

• http://kb.mozillazine.org/Show_hidden_files_and_folders

IconCache.db is rebuilt, but problem remains.

Perhaps icon cache is not to blame because

Mozilla Corporation becomes Microsoft Corporation,

and

If I click on Set this program as default, files of these types are opened by Windows Media Player, not by Firefox: htm, html, shtml, xht, xhtml.

So, I assume something somewhere in registry must have gone wrong.

Also, I notice that the following registry key contains nothing:

HKEY_LOCAL_MACHINE\SOFTWARE\Mozilla\Firefox

Is that a problem?

You can try to uninstall and reinstall Firefox, possibly as Administrator.

Do a clean reinstall and delete the Firefox program folder before (re)installing a fresh copy of the current Firefox release.

Download a fresh Firefox copy and save the file to the desktop.

• Firefox 24: http://www.mozilla.org/en-US/firefox/all.html

Uninstall your current Firefox version, if possible, to cleanup the Windows registry and settings in security software.

• Do NOT remove personal data when you uninstall your current Firefox version, because all profile folders will be removed and you lose personal data like bookmarks and passwords from profiles of other Firefox versions.

Remove the Firefox program folder before installing that newly downloaded copy of the Firefox installer.

• (32 bit Windows) "C:\Program Files\Mozilla Firefox\"
• (64 bit Windows) "C:\Program Files (x86)\Mozilla Firefox\"

• It is important to delete the Firefox program folder to remove all the files and make sure that there are no problems with files that were leftover after uninstalling.
• http://kb.mozillazine.org/Uninstalling_Firefox

Your bookmarks and other personal data are stored in the Firefox profile folder and won't be affected by an uninstall and (re)install, but make sure that "remove personal data" is NOT selected when you uninstall Firefox.

• http://kb.mozillazine.org/Profile_folder_-_Firefox
• http://kb.mozillazine.org/Profile_backup

• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Clean_reinstall

I don't know if the extensions I use for version 19.2 suit the latest version. So, I just re-installed 19.2, and all is well now. Thank you very much for your help.

After the re-installation, I noticed there is a string value Firefox under

HKEY_LOCAL_MACHINE\SOFTWARE\RegisteredApplications

This registry key contains all the program names listed in Set your default programs. So, I guess that if the string Firefox points to Windows Media Player, I get the trouble.