https://support.mozilla.org/en-US/kb/fix-problems-connecting-websites-after-updating

I had already tried all of those solutions (and any other ones already addressed on the support website) . I think the problem may be a registry entry somewhere, but have no idea where to start. Note that IE9 and the latest versions of Safari and Opera all fail to connect. I have already added the latest Service Pack to Windows Vista as well as all of the latest updates. Since the failure occurs on all later versions of browsers, it seems like it could be a subsystem issue and not related to a particular browser. Just a guess though. Regardless of all that, Firefox should be able to load a local network node (i.e. 192.168.1.1), don't you think?

Try to boot the computer in Windows Safe mode with network support (press F8 on the boot screen) as a test to see if that helps.

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

• 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
• Kasperky Free Security Scan:
  http://www.kaspersky.com/security-scan

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

• http://support.kaspersky.com/viruses/solutions?qid=208280684

See also:

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