Sounds like you might have a phishing or cookie-retention virus in one of the Firefox plug-ins.
Before proceeding I strongly urge you to BACKUP ANY AND ALL PERSONAL DATA THAT YOU CANNOT AFFORD TO LOSE TO EXTERNAL MEDIA!!! THE FOLLOWING PROCEDURES CAN CAUSE PERMANENT DATA LOSS!!
CCleaner will not remove this. Don't know what anti-virus you are using, but I suggest you go to trendmicro.com and run their free Housecall online scanner. After that, download the free Malwarebytes from malwarebytes.org, and do a free local anti-spyware scan and removal. Retest your browser and search engines.
If problem persists, run SAFE MODE on your computer and utilize disk cleanup and remove all PASSWORDS, COOKIES, AUTO-FORM DATA, and everything else except Volume Shadow Data (used for Restore Points).
After completing these tasks, and retesting shows the problem persists, I suggest you "rollback" your system to a point in time prior to this problem occurring. Bear in mind that if this problem has been around longer than 5 months; System Restore cannot rollback your computer further back than this.
If SYSTEM RESTORE fails to resolve it, it's very likely that your hard drive has failed or begun to fail, and you will need to test it with SEATOOLS. Post back if you need help doing this. If SEATOOLS returns errors, your hard drive has failed and must be replaced. If your computer is 3 years old or older, this is the #1 hardware failure if it's a desktop PC. If it's a laptop and older than 2 years; same thing.
After testing your hard drive or replacing it if it failed SEATOOLS, you will need to perform a WINDOWS RESET or WINDOWS RECOVERY from legit Factory RECOVERY MEDIA. This should resolve your problem.
I also suggest that you switch to another browser from Firefox, to Internet Explorer, Chrome, or Safari, as Firefox has had problems with virus-infested plug-ins for almost 2 years now. I move all of my Customers off from it these days.
Best of luck,
<<<BIGBEARJEDI>>>
