You may be infected with malware.

Do a malware check with some malware scanning programs.
You need to scan with all programs because each program detects different malware.
Make sure that you update each program to get the latest version of their databases before doing a scan.

• http://www.malwarebytes.org/mbam.php - Malwarebytes' Anti-Malware
• http://www.superantispyware.com/ - SuperAntispyware
• http://www.microsoft.com/windows/products/winfamily/defender/default.mspx - Windows Defender: Home Page
• http://www.safer-networking.org/en/index.html - Spybot Search & Destroy
• http://www.lavasoft.com/products/ad_aware_free.php - Ad-Aware Free

See also:

• "Spyware on Windows": http://kb.mozillazine.org/Popups_not_blocked

If using the above listed scanners does not fix it or if you are blocked from installing those scanners then ask advice on one of the forums that specialize in malware removal mentioned in the Popups_not_blocked article.

Troubleshooting extensions and themes

• https://support.mozilla.com/en-US/kb/Troubleshooting%20extensions%20and%20themes

Clear Cookies & Cache

• https://support.mozilla.com/en-US/kb/Template:clearCookiesCache

Restore the default home page

• https://support.mozilla.com/en-US/kb/How%20to%20set%20the%20home%20page#w_restore-the-default-home-page

• go to Tools Menu -> Options -> Content -> place Checkmark on Block Pop-ups windows -> click Exceptions... button and click Remove All
• go to Tools Menu -> Options -> Privacy -> Firefox will: select Remember History
• go to Tools Menu -> Options -> Security -> place Checkmarks on ---> (1) Warn me when websites try to install add-ons (2) Block Reported Attack Sites (3) Clock Reported Web Forgeries
• go to Tools Menu -> Options -> Advanced -> General -> Remove Checkmark from Warn me when websites try to redirect or reload the page
• go to Tools Menu -> Options -> Advanced -> Encryption ---> under Protocols place Checkmarks on -> (1) Use SSL 3.0 (2) Use TLS 1.0 ---> under Certificates select Ask me Every Time
• click OK on Options window -> Restart Firefox

Check and tell if its working.

Thanks for the previous two answers. I appreciate it, but they were not successful. However, I do seem to have solved the problem - for anyone else who may be experiencing this, we downloaded and ran TDSSKILLER. This is described as an Anti-Rootkit Utility. Googling it will show you places to download it for free. So far its working.