Unable to search or add new engines
From MozillaZine Knowledge Base
Unable to search
If the problem is not resolved, exit Firefox again, go back to your Firefox profile folder and delete (or rename) the file "formhistory.sqlite" (also delete "formhistory.sqlite-journal", "formhistory.sqlite.corrupt" and "formhistory.dat", if they exist). This may resolve the issue but will remove all Saved Form data from Firefox. 
If you still have search problems after restarting Firefox, check the following:
A Firefox extension may be causing your search problem. For more information, see the Problematic extensions article.
Spyware and malware
Spyware and other malicious software (malware), including variants of the Vundo/Virtumonde trojan, can cause certain sites to never finish loading and Google, Yahoo!, or other search engines may fail.     For example, after entering a search in Google, "Waiting for www.google.com..." may remain in the status bar and no results will be returned. Your security software may not detect the malware so you should install and run another application that can scan your system and remove the malware or seek help from a forum specializing in malware removal. Some recommended anti-malware applications and help forums are listed here.
Searches being redirected
If clicking on a certain search result redirects you to an unwanted site, the legitimate website for your search result may have been compromised. When your search result takes you to that site, it determines the "referring" page and, if it’s from a link in a Google (or other) search engine's results page, then you are automatically re-directed to malicious websites that are totally unrelated to the original site. In such cases you can manually type in the URL instead of clicking the search result link (or try another search engine).   
Note: If typing an incorrect URL in the Location Bar redirects you to a results page from an unwanted search engine, this is a different issue. Your ISP (Internet Service Provider) may be intercepting the failed DNS requests, as discussed here.
If multiple search results are redirected to unwanted sites or if your searches are "hijacked" by an unwanted search engine (such as Ask.com), check for problematic extensions, disable or uninstall any added extensions and remove any added toolbars that you suspect may be interfering with Web searches. You may also need to switch back to your preferred search engine in the Firefox Search Bar and reset any preferences in about:config that refer to the removed add-on or unwanted search engine (e.g., keyword.URL). 
If the problem persists, go through the standard diagnostic steps. A clean reinstall will remove components that another software installation may have added to Firefox.  You should also check for malware, especially if you are having other issues such as security-related websites being blocked. Malware added to the Firefox installation directory "extensions" folder or detected by Firefox via the Windows registry can cause redirects to unwanted sites. See the forum topics here and here for more information.
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