To my knowledge, a plugin does not have the power to do this, so the most likely culprit is an extension. Here's my suggested procedure for tracking down and cleaning up bad add-ons and other hijackers. I know it seems long, but it's really not that bad.

(1) Open the Windows Control Panel, Uninstall a Program. After the list loads, click the "Installed on" column heading to group the infections, I mean, additions, by date. This can help in smoking out undisclosed bundle items that snuck in with some software you agreed to install. Be suspicious of everything you do not recognize/remember, as malware often uses important or innocent sounding names to discourage you from removing it. Take out as much trash as possible here.

(2) Open Firefox's Add-ons page using either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons
• in the Windows "Run" dialog, type or paste
  firefox.exe "about:addons"

In the left column, click Plugins. Set nonessential and unrecognized plugins to "Never Activate".

In the left column, click Extensions. Then, if in doubt, disable (or Remove, if possible) unrecognized and unwanted extensions.

Often a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Any improvement?

(3) You can search for remaining issues with the scanning/cleaning tools listed in our support article: Troubleshoot Firefox issues caused by malware. These on-demand scanners are free and take considerable time to run. If they finish quickly and especially if they require payment, you may have a serious infection. I suggest the specialized forums listed in the article in that case.

Success?

Also, if the pattern is that you can switch it successfully until you exit Firefox and start it up again, please check the user.js section of this article: How to fix preferences that won't save.

After the problem is fixed, Bookmark and use this; Download the 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.

@FredMcD The search reset is not working (is not accepted) bij Firefox Developer Edition v.41, 64bit. I am so sorry because your advice was really well meant and solid but only for older versions of Firefox.

Hey Guys, Thanks very much, the solution for me was:

Refresh Firefox to fix the problem

The easiest way to solve this problem is to restore Firefox to its default state while saving your essential information. Besides resetting all preferences to default values, a Firefox refresh will also fix a wide range of other issues, including problems caused by extensions or with data and settings that are stored in other files in your Firefox profile. If you'd like to try a more precise fix, skip this section and try the solutions below. Note: When using the refresh feature, your bookmarks, browsing history, open tabs, windows, passwords, cookies and web form auto-fill information will be saved. However, your extensions and themes will be removed and your preferences will be reset. Learn more.

   Click this Refresh Firefox button directly, if you are viewing this page in Firefox (it won't work if you are using a different browser). You will also find a Refresh button on the top right corner of the Firefox about:support Troubleshooting Information page.
   To continue, click Refresh Firefox in the confirmation window that opens.
   Firefox will close to refresh itself. When finished, a window will list your imported information. Click Finish and Firefox will open.

After I did this I created new profiles and the problem was solved.

Thanks for directing me in the right direction.

That was very good work. Well Done. Please flag your last post as Solved Problem so others will know.