Try Firefox Safe Mode to see if the problem goes away. Safe Mode is a troubleshooting mode, which disables most add-ons.

(If you're not using it, switch to the Default theme.)

• Open the Help menu and click on the Restart with Add-ons Disabled... menu item while Firefox is running.

Once you get the pop-up, just select "'Start in Safe Mode"

If the issue is not present in Firefox Safe Mode, your problem is probably caused by an extension, and you need to figure out which one. Please follow the Troubleshoot extensions, themes and hardware acceleration issues to solve common Firefox problems article for that.

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

Please report back for more support.

Note that your System Details List shows that you have a user.js file in the profile folder to initialize some prefs on each start of Firefox.

The user.js file is only present if you or other software has created it, so normally it wouldn't be there. You should check its content with a plain text editor if you didn't create this file yourself.

The user.js file is read each time you start Firefox and initializes preferences to the value specified in this file, so preferences set via user.js can only be changed temporarily for the current session.

• http://kb.mozillazine.org/Preferences_not_saved

Check the connection settings.

• Tools > Options > Advanced > Network : Connection > Settings
• https://support.mozilla.org/kb/Options+window+-+Advanced+panel

If you do not need to use a proxy to connect to internet then try to select "No Proxy" if "Use the system proxy settings" or one of the others do not work properly.

See "Firefox connection settings":

• https://support.mozilla.org/kb/Firefox+cannot+load+websites+but+other+programs+can

Do a malware check with some malware scanning programs on the Windows computer.
Please 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.

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

Normally, web servers redirect using a 301 (moved permanently) or 302 (moved temporarily) status code. However, sometimes they send a 307 (temporary redirect) and Firefox has a special warning for that. Based on searching some past threads, I think you might be seeing that special warning.

Getting this error frequently may indicate that the page is making a lot of background requests. If you trust the requests (hard to know, I guess, without more information), you can disable the warning. Here's how:

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the search box that appears above the list, type or paste redi and pause while the list is filtered

(3) Double-click network.http.prompt-temp-redirect to switch its value from true (the default) to false.

This doesn't answer the question of what is causing the redirect. Perhaps it's a content filter feature of your new router??

References:

• I receive this usually in facebook only. " This web page is being redirected to a new location. Would you like to resend the form data you have typed to the new location?" How can I stop this? - related to filtering/protection service

• 818850 – The dialog "...new location..." is too annoying and is misleading about the page it comes from - information about the bug tracking system:
  • Bugzilla Etiquette
  • Voting