Try Firefox Safe Mode to see if the problem goes away.

If Firefox is open, you can restart in Firefox Safe Mode from the Help menu:

• Click the menu button , click Help and select Restart with Add-ons Disabled.

If Firefox is not running, you can start Firefox in Safe Mode as follows: Quit Firefox, go to your Terminal and run firefox -safe-mode
(you may need to specify the Firefox installation path e.g. /usr/lib/firefox)

When the Firefox Safe Mode window appears, select "Start in Safe Mode".

If the issue is not present in Firefox Safe Mode, your problem is probably caused by an extension, theme, or hardware acceleration. Please follow the steps in the Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems article to find the cause.

To exit Firefox Safe Mode, just close Firefox and wait a few seconds before opening Firefox for normal use again.

Clear the cache and remove cookies only from websites that cause problems.

"Clear the Cache":

• Firefox/Tools > Options > Advanced > Network > Cached Web Content: "Clear Now"

"Remove Cookies" from sites causing problems:

• Firefox/Tools > Options > Privacy > "Use custom settings for history" > Cookies: "Show Cookies"

You can remove all data stored in Firefox from a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History > Show All History" or "View > Sidebar > History") or via the about:permissions page.

Using "Forget About This Site" will remove all data stored in Firefox from that domain like bookmarks, cookies, passwords, cache, history, and exceptions, so be cautious and if you have a password or other data from that domain that you do not want to lose then make sure to backup this data or make a note.

You can't recover from this 'forget' unless you have a backup of the involved files.

It doesn't have any lasting effect, so if you revisit such a 'forgotten' website then data from that website will be saved once again.

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
• https://support.mozilla.org/kb/troubleshoot-firefox-issues-caused-malware

It is correct that http://www.google.com/ replies with a "302" redirect to the HTTPS site with the explanatory parameter. However, what is strange is that Firefox is pausing to show you that redirect instead of simply following it. To me an add-on is the most likely explanation for that special handling.

For what it's worth, I have attached the navigation I see in the Web Console, Network panel, for going to http://google.com/