You can check the startup setting:

• Tools > Options > General > Startup: "When Firefox Starts":
  "Show my windows and tabs from last time"
  "Show my home page"
  "Show a blank page"

You can check for problems with preferences.

Delete possible user.js and numbered prefs-##.js files and rename (or delete) the prefs.js file to reset all prefs to the default value including prefs set via user.js and prefs that are no longer supported in the current Firefox release.

• http://kb.mozillazine.org/Preferences_not_saved
• http://kb.mozillazine.org/Resetting_preferences

You can check for problems with the sessionstore.js file in the Firefox profile folder that store session data.

• Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
• http://kb.mozillazine.org/Profile_folder_-_Firefox
• http://kb.mozillazine.org/Multiple_profile_files_created

Deleting sessionstore.js will cause App Tabs and Tab Groups and open and closed (undo) tabs to get lost and you will have to recreate them (make a note or bookmark them if possible).

Separate Issue; Your System Details shows;

Installed Plug-ins

Adobe PDF Plug-In For Firefox and Netscape 11.0.10 Adobe PDF Plug-In For Firefox and Netscape 11.0.11
Having more than one version of a program may cause issues. You must remove the older programs. Then get the current full installer.

Once you have the above problem settled,

Bookmark and use this; Mozilla Search Reset {web link} This add-on is very simple: on installation, it backs up and then resets your search preferences and home page to their default values, and then uninstalls itself. This affects the search bar, URL bar searches, and the home page.

Settings Guard for Firefox {web link} Detects and resets changes to settings that are frequently done by add-ons and application installers.