If you get a pop-up message asking to update Firefox or plugins then such a message is likely a scam and you should never respond to such an alert to avoid getting infected with malware.

• Only update Firefox via "Help > About" or by downloading and installing Firefox from the Mozilla server and never via a pop-up or link on a web page.
• Plugins should only be updated via the plugin itself or by visiting the home page of the plugin.

Do a malware check with several malware scanning programs on the Windows computer. Please scan with all programs because each program detects different malware. All these programs have free versions.

Make sure that you update each program to get the latest version of their databases before doing a scan.

• Malwarebytes' Anti-Malware:
  http://www.malwarebytes.org/mbam.php
• AdwCleaner:
  http://www.bleepingcomputer.com/download/adwcleaner/
  http://www.softpedia.com/get/Antivirus/Removal-Tools/AdwCleaner.shtml
• SuperAntispyware:
  http://www.superantispyware.com/
• Microsoft Safety Scanner:
  http://www.microsoft.com/security/scanner/en-us/default.aspx
• Windows Defender:
  http://windows.microsoft.com/en-us/windows/using-defender
• Spybot Search & Destroy:
  http://www.safer-networking.org/en/index.html
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

You can also do a check for a rootkit infection with TDSSKiller.

• Anti-rootkit utility TDSSKiller:
  http://support.kaspersky.com/5350?el=88446

See also:

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

You may have an unwanted extension that is creating the pop-ups. Try this:

Disable ALL nonessential or unrecognized extensions on the Add-ons page. Either:

• Ctrl+Shift+a
• "3-bar" menu button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Usually 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.

Does that shut them down?

Because these annoying extensions often sneak onto your computer as part of a bundle with some free software, you may need to remove them through the Windows Control Panel. Open Add/Remove programs, and click the "Installed on" column heading to group the entries by date. Then take out as much trash as you can.

Finally, consider supplementing your regular security scans with some of the free tools in our support article: Troubleshoot Firefox issues caused by malware.

Any luck? If the problem persists, can you spot any pattern to the pop-ups, sometimes the adware puts its name on them.

By the way, you can still disable JavaScript, but it's a little harder now because you need to go either into the developer tools or about:config. To make it easier to switch on and off, you can get an extension that adds a dedicated toolbar button. This one is popular: https://addons.mozilla.org/firefox/addon/quickjava/